CHAPTER 4
THE ART OF MODELING WITH SPREADSHEETS
SOLUTION TO SOLVED PROBLEMS
4.S1 Production and Inventory Planning Model
Surfs Up produces high-end surfboards. Their production facility can produce at most 50 boards
per month. A challenge faced by Surfs Up is that their demand is highly seasonal. Demand
exceeds production capacity during the warm summer months, but is very low in the winter
months. To meet the high demand during the summer, Surfs Up typically produces more surf
boards than are needed in the winter months and then carries inventory into the summer months.
The production cost of a surfboard is $125. The boards are sold for $200. Because of storage
cost and the opportunity cost of capital, each board held in inventory from one month to the next
incurs a cost of $5 per board. Since demand is uncertain, Surfs Up would like to maintain an
ending inventory (safety stock) of at least 10 boards during the warm months (May–September)
and at least 5 boards during the other months (October–April). It is now the start of January and
Surfs Up has 5 boards in inventory. The forecast of demand over the next 12 months is shown in
the table below. Formulate and solve a linear programming model in a spreadsheet to determine
how many surfboards should be produced each month to maximize total profit.
Jan
Feb
Mar
Apr
May
Jun
July
Aug
Sep
Oct
Nov
Dec
10
14
15
20
45
65
85
85
40
30
15
15
This is a dynamic problem with 12 time periods (months). The activities are the production
quantities in each of the 12 months.
1
To get started, we sketch a spreadsheet model. Each of the 12 months will be a separate column
in the spreadsheet. For each month, the production quantity (a changing cell) must be no more
than the maximum production quantity (50). Using on-hand inventory and current month
production, there will be a quantity of surf boards available for sale that must be greater than or
equal to the forecasted sales. The ending inventory at the end of each month must be at least the
minimum safety stock level. Each month will generate revenue, incur production costs and
inventory holding costs, and achieve a resulting profit. The goal will be to maximize the total
profit over all 12 months. This leads to the following sketch of a spreadsheet model.
Production Cost
Selling Price
Holding Cost
Starting Inventory
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
Production
<=
Maximum
Available for Sale
>=
Forecasted Sales
Ending Inventory
>=
Safety Stock
Total
Revenue
Production Cost
Holding Cost
Profit
2
The amount available for sale will be the ending inventory from the previous month (or the
starting inventory for January) plus whatever is produced in that month. The ending inventory
will be the previous month’s ending inventory plus production minus sales. The revenue will
equal the selling price times forecasted sales. The production cost will be the production quantity
times the unit production cost. The holding cost will equal the ending inventory times the unit
holding cost. The monthly profit will be revenue minus production cost minus holding cost.
Finally, the total profit will be the sum of the monthly profits. Arbitrary production quantities of
25 each month leads to the following spreadsheet.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
B
Production Cost
Selling Price
Holding Cost
Starting Inventory
Production
Maximum
Available for Sale
Forecasted Sales
Ending Inventory
Safety Stock
C
$125
$200
$5
5
D
E
F
G
H
I
J
K
L
M
N
Jan
25
<=
50
Feb
25
<=
50
Mar
25
<=
50
Apr
25
<=
50
May
25
<=
50
Jun
25
<=
50
Jul
25
<=
50
Aug
25
<=
50
Sep
25
<=
50
Oct
25
<=
50
Nov
25
<=
50
Dec
25
<=
50
30
>=
10
45
>=
14
56
>=
15
66
>=
20
71
>=
45
51
>=
65
11
>=
85
-49
>=
85
-109
>=
40
-124
>=
30
-129
>=
15
-119
>=
15
20
>=
5
31
>=
5
41
>=
5
46
>=
5
26
>=
10
-14
>=
10
-74
>=
10
-134
>=
10
-149
>=
10
-154
>=
5
-144
>=
5
-134
>=
5
$2,800
$3,125
$155
-$480
$3,000
$3,125
$205
-$330
$4,000
$3,125
$230
$645
$9,000
$3,125
$130
$5,745
$8,000
$3,125
-$745
$5,620
$6,000
$3,125
-$770
$3,645
$3,000
$3,125
-$720
$595
$3,000
$3,125
-$670
$545
Revenue $2,000
Production Cost $3,125
Holding Cost $100
Profit -$1,225
B
Production Cost 125
Selling Price 200
Holding Cost 5
Starting Inventory 5
C
$13,000 $17,000 $17,000
$3,125 $3,125 $3,125
-$70
-$370
-$670
$9,945 $14,245 $14,545
D
EFGHIJKLM
N
Feb
Dec
50
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
25
25
25
25
25
25
25
25
25
25
<=
<=
<=
<=
<=
<=
<=
<=
<=
50
50
50
50
50
50
50
50
50
50
Available for Sale =StartingInventory+Production
>=
Forecasted Sales 10
=C17+Production
>=
14
=D17+Production
=E17+Production
=F17+Production
=G17+Production
=H17+Production
=I17+Production
=J17+Production
=K17+Production
=L17+Production
=M17+Production
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
15
20
45
65
85
85
40
30
15
15
Ending Inventory =AvailableForSale-ForecastedSales
>=
Safety Stock 5
=AvailableForSale-ForecastedSales =AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
5
5510
10
10
10
10
555
Jan
Production 25
25
<=
Maximum 50
Revenue =SellingPrice*ForecastedSales
Production Cost =ProductionCost*Production
Holding Cost =HoldingCost*EndingInventory
Profit =C22-C23-C24
<=
=SellingPrice*ForecastedSales
=ProductionCost*Production
=HoldingCost*EndingInventory
=D22-D23-D24
3
O
Total
$87,800
$37,500
-$3,195
$53,495
O
<=
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=E22-E23-E24
=F22-F23-F24
=G22-G23-G24
=H22-H23-H24
=I22-I23-I24
=J22-J23-J24
=K22-K23-K24
=L22-L23-L24
=M22-M23-M24
=N22-N23-N24
Total
=SUM(C22:N22)
=SUM(C23:N23)
=SUM(C24:N24)
=SUM(C25:N25)
The Solver information and solved spreadsheet are shown below.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
B
C
Production Cost $125
Selling Price $200
Holding Cost $5
Starting Inventory
5
Production
Maximum
Available for Sale
Forecasted Sales
Ending Inventory
Safety Stock
D
E
F
G
H
I
J
K
L
M
N
Jan
10
<=
50
Feb
34
<=
50
Mar
50
<=
50
Apr
50
<=
50
May
50
<=
50
Jun
50
<=
50
Jul
50
<=
50
Aug
50
<=
50
Sep
40
<=
50
Oct
25
<=
50
Nov
15
<=
50
Dec
15
<=
50
15
>=
10
39
>=
14
75
>=
15
110
>=
20
140
>=
45
145
>=
65
130
>=
85
95
>=
85
50
>=
40
35
>=
30
20
>=
15
20
>=
15
5
>=
5
25
>=
5
60
>=
5
90
>=
5
95
>=
10
80
>=
10
45
>=
10
10
>=
10
10
>=
10
5
>=
5
5
>=
5
5
>=
5
Total
Revenue $2,000 $2,800 $3,000 $4,000 $9,000 $13,000 $17,000 $17,000 $8,000 $6,000 $3,000 $3,000 $87,800
Production Cost $1,250 $4,250 $6,250 $6,250 $6,250 $6,250 $6,250 $6,250 $5,000 $3,125 $1,875 $1,875 $54,875
Holding Cost $25
$125
$300
$450
$475
$400
$225
$50
$50
$25
$25
$25
$2,175
Profit $725 -$1,575 -$3,550 -$2,700 $2,275 $6,350 $10,525 $10,700 $2,950 $2,850 $1,100 $1,100 $30,750
Range Nam e
Avail able ForSal e
Endi ngIn ve ntory
Fore cas tedSa les
Holdi ngCost
Maximum
Produ cti on
Produ cti onCost
Safe tyStock
Sell ingPri ce
StartingInvento ry
TotalProfit
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
O
B
Production Cost 125
Selling Price 200
Holding Cost 5
Starting Inventory 5
C
Cells
C13:N13
C17:N17
C15:N15
C5
C11:N11
C9:N9
C3
C19:N19
C4
C6
O25
D
EFGHIJKLM
N
Feb
Dec
50
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
25
25
25
25
25
25
25
25
25
25
<=
<=
<=
<=
<=
<=
<=
<=
<=
50
50
50
50
50
50
50
50
50
50
Available for Sale =StartingInventory+Production
>=
Forecasted Sales 10
=C17+Production
>=
14
=D17+Production
=E17+Production
=F17+Production
=G17+Production
=H17+Production
=I17+Production
=J17+Production
=K17+Production
=L17+Production
=M17+Production
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
15
20
45
65
85
85
40
30
15
15
Ending Inventory =AvailableForSale-ForecastedSales
>=
Safety Stock 5
=AvailableForSale-ForecastedSales =AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
=AvailableForSale-ForecastedSales
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
5
5510
10
10
10
10
555
Jan
Production 25
25
<=
Maximum 50
Revenue =SellingPrice*ForecastedSales
Production Cost =ProductionCost*Production
Holding Cost =HoldingCost*EndingInventory
Profit =C22-C23-C24
<=
=SellingPrice*ForecastedSales
=ProductionCost*Production
=HoldingCost*EndingInventory
=D22-D23-D24
O
<=
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=SellingPrice*ForecastedSales
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=ProductionCost*Production
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=HoldingCost*EndingInventory
=E22-E23-E24
=F22-F23-F24
=G22-G23-G24
=H22-H23-H24
=I22-I23-I24
=J22-J23-J24
=K22-K23-K24
=L22-L23-L24
=M22-M23-M24
=N22-N23-N24
Total
=SUM(C22:N22)
=SUM(C23:N23)
=SUM(C24:N24)
=SUM(C25:N25)
The values in Production (C9:N9) show how many surf boards Surfs Up should produce each
month so as to achieve the maximum profit of $30,750.
4
4.S2 Aggregate Planning: Manpower Hiring/Firing/Training
Cool Power produces air conditioning units for large commercial properties. Due to the low cost
and efficiency of its products, the company has been growing from year to year. Also, due to
seasonality in construction and weather conditions, production requirements vary from month to
month. Cool Power currently has 10 fully trained employees working in manufacturing. Each
trained employee can work 160 hours per month and is paid a monthly wage of $4000. New
trainees can be hired at the beginning of any month. Due to their lack of initial skills and
required training, a new trainee only provides 100 hours of useful labor in their first month, but
are still paid a full monthly wage of $4000. Furthermore, because of required interviewing and
training, there is a $2500 hiring cost for each employee hired. After one month, a trainee is
considered fully trained. An employee can be fired at the beginning of any month, but must be
paid two weeks of severance pay ($2000). Over the next 12 months, Cool Power forecasts the
labor requirements shown in the table below. Since management anticipates higher requirements
next year, Cool Power would like to end the year with at least 12 fully trained employees. How
many trainees should be hired and/or workers fired in each month to meet the labor
requirements at the minimum possible cost? Formulate and solve a linear programming
spreadsheet model.
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1600
2000
2000
2000
2800
3200
3600
3200
1600
1200
800
800
This is a dynamic problem with 12 time periods (months). The activities are the number of
workers to hire and fire in each of the 12 months.
5
To get started, we sketch a spreadsheet model. Each of the 12 months will be a separate column
in the spreadsheet. For each month, there are changing cells for both the number of workers hired
and fired. Based on the values of these changing cells, we can determine the number of trainees
and trained employees. The number of labor hours generated by the employees must be at least
the required labor hours each month. Finally, labor costs (for trainees and the trained workforce),
hiring cost, and severance pay leads to a total monthly cost. The goal will be to minimize the
total cost over all 12 months. This leads to the following sketch of a spreadsheet model.
Labor Monthly Wage
Hiring Cost
Severance Pay
Labor Hours/Trainee/Month
Labor Hours/Trained Worker/Month
Starting Trained Workforce
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
Workers Hired
Workers Fired
Minimum to
Start the
Next Year
Trainees
Trained Employees
>=
Labor Hours Available
>=
Required Labor Hours
Total
Labor Cost (Trainees)
Labor Cost (Trained Workforce)
Hiring Cost
Severance Pay
Total Cost
6
When an employee is first hired, he or she is a trainee for one month before becoming a fullytrained employee. Therefore, the number of trainees (row 14) is equal to the number of workers
hired in that month, while the number of trained employees (row 15) is the number of trained
employees and trainees from the previous month minus any employee that is fired. The labor
hours available in each month equals the sumproduct of the labor hours provided by each type of
worker (trained or trainees) with the number of each type of employee. The labor costs in each
month are the monthly wage multiplied by the number of employees. The hiring cost is the unit
hiring cost multiplied by the number of workers hired. The severance pay is the unit severance
cost multiplied by the number of workers fired. Then, the total monthly cost is the sum of the
labor costs, hiring cost, and severance pay. Finally, the total cost will be the sum of the monthly
costs. For arbitrary values of workers hired and fired each month, this leads to the following
spreadsheet.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
B
C
Labor Monthly Wage $4,000
Hiring Cost $2,500
Severance Pay $2,000
Labor Hours/Trainee/Month
100
Labor Hours/Trained Worker/Month
160
Starting Trained Workforce
10
D
E
F
G
H
I
J
K
L
M
N
Workers Hired
Workers Fired
Jan
2
0
Feb
2
0
Mar
2
0
Apr
2
0
May
2
0
Jun
2
0
Jul
2
0
Aug
0
3
Sep
0
3
Oct
0
3
Nov
2
0
Dec
2
0
Trainees
Trained Employees
2
10
2
12
2
14
2
16
2
18
2
20
2
22
0
21
0
18
0
15
2
15
2
17
1800
>=
1600
2120
>=
2000
2440
>=
2000
2760
>=
2000
3080
>=
2800
3400
>=
3200
3720
>=
3600
3360
>=
3200
2880
>=
1600
2400
>=
1200
2600
>=
800
2920
>=
800
$8,000
$40,000
$5,000
$0
$53,000
$8,000
$48,000
$5,000
$0
$61,000
$8,000
$56,000
$5,000
$0
$69,000
$8,000
$64,000
$5,000
$0
$77,000
$8,000
$72,000
$5,000
$0
$85,000
Labor Hours Available
Required Labor Hours
Labor Cost (Trainees)
Labor Cost (Trained Workforce)
Hiring Cost
Severance Pay
Total Cost
$8,000
$8,000
$0
$0
$0
$8,000
$80,000 $88,000 $84,000 $72,000 $60,000 $60,000
$5,000
$5,000
$0
$0
$0
$5,000
$0
$0
$6,000 $6,000 $6,000
$0
$93,000 $101,000 $90,000 $78,000 $66,000 $73,000
B
Labor Monthly Wage 4000
Hiring Cost 2500
Severance Pay 2000
Labor Hours/Trainee/Month 100
Labor Hours/Trained Worker/Month 160
Starting Trained Workforce 10
C
Jan
Workers Hired 2
Workers Fired 0
Trainees =WorkersHired
Trained Employees =StartingTrainedWorkforce-WorkersFired
$8,000
$68,000
$5,000
$0
$81,000
DEFGHIJKLMN
O
P
>=
Minimum to
Start the
Next Year
12
Total
$72,000
$792,000
$45,000
$18,000
$927,000
O
P
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
102430.999999999999998
0002.00000000006961
0
000000310
000
Minimum to
Start the
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
Next Year
=C15+C14-WorkersFired
=D15+D14-WorkersFired
=E15+E14-WorkersFired
=F15+F14-WorkersFired
=G15+G14-WorkersFired
=H15+H14-WorkersFired
=I15+I14-WorkersFired
=J15+J14-WorkersFired
=K15+K14-WorkersFired
=L15+L14-WorkersFired
=M15+M14-WorkersFired
>=
12
Labor Hours Available =SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWorker,C14:C15) =SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWor
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWo
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWo
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedW
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedW
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrained
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTraine
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrain
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrain
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTra
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTra
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
Required Labor Hours 1600
2000
2000
2000
2800
3200
3600
3200
1600
1200
800
800
Labor Cost (Trainees) =LaborMonthlyWage*Trainees
Labor Cost (Trained Workforce) =LaborMonthlyWage*TrainedEmployees
Hiring Cost =HiringCost*WorkersHired
Severance Pay =SeverancePay*WorkersFired
Total Cost =SUM(C22:C25)
7
Total
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=SUM(C22:N22)
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=SUM(C23:N23)
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=SUM(C24:N24)
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SUM(C25:N25)
=SUM(D22:D25)
=SUM(E22:E25)
=SUM(F22:F25)
=SUM(G22:G25)
=SUM(H22:H25)
=SUM(I22:I25)
=SUM(J22:J25)
=SUM(K22:K25)
=SUM(L22:L25)
=SUM(M22:M25)
=SUM(N22:N25)
=SUM(C26:N26)
The Solver information is shown below, followed by the solved spreadsheet.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
B
C
Labor Monthly Wage $4,000
Hiring Cost $2,500
Severance Pay $2,000
Labor Hours/Trainee/Month
100
Labor Hours/Trained Worker/Month
160
Starting Trained Workforce
10
D
E
F
G
H
I
J
K
L
M
N
Jan
Workers Hired 2.1E-11
Workers Fired
0
Feb
4
0
Mar
0
0
Apr
0
0
May
6
0
Jun
2
0
Jul
1
0
Aug
0
3
Sep
0
10
Oct
0
0
Nov
2
0
Dec
0
0
Trainees 2.1E-11
Trained Employees
10
4
10
0
14
0
14
6
14
2
20
1
22
0
20
0
10
0
10
2
10
0
12
2000
>=
2000
2240
>=
2000
2240
>=
2000
2840
>=
2800
3400
>=
3200
3620
>=
3600
3200
>=
3200
1600
>=
1600
1600
>=
1200
1800
>=
800
1920
>=
800
Labor Hours Available
Required Labor Hours
1600
>=
1600
Labor Cost (Trainees)
$0
$16,000
$0
$0
$24,000 $8,000
$4,000
Labor Cost (Trained Workforce) $40,000 $40,000 $56,000 $56,000 $56,000 $80,000 $88,000
Hiring Cost
$0
$10,000
$0
$0
$15,000 $5,000
$2,500
Severance Pay
$0
$0
$0
$0
$0
$0
$0
Total Cost $40,000 $66,000 $56,000 $56,000 $95,000 $93,000 $94,500
$0
$0
$0
$80,000 $40,000 $40,000
$0
$0
$0
$6,000 $20,000
$0
$86,000 $60,000 $40,000
Range Na me
Hirin gCost
La borHours Availa ble
La borHours PerTrai nedWorke r
La borHours PerTrai nee
La borMonthlyWag e
Mini mumToStartNe xtYear
Requ iredL aborHou rs
Severa nce Pay
Sta rting Train edWo rkfo rce
To talCos t
Tra ined Emplo ye es
Tra inee s
Wo rkers Fired
Wo rkers Hi red
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
B
Labor Monthly Wage 4000
Hiring Cost 2500
Severance Pay 2000
Labor Hours/Trainee/Month 100
Labor Hours/Trained Worker/Month 160
Starting Trained Workforce 10
C
Jan
Workers Hired 2
Workers Fired 0
Trainees =WorkersHired
Trained Employees =StartingTrainedWorkforce-WorkersFired
O
P
>=
Minimum to
Start the
Next Year
12
Total
$8,000
$0
$60,000
$40,000 $48,000 $664,000
$5,000
$0
$37,500
$0
$0
$26,000
$53,000 $48,000 $787,500
Cells
C4
C17:N1 7
C7
C6
C3
P15
C19:N1 9
C5
C8
O26
C15:N1 5
C14:N1 4
C12:N1 2
C11:N1 1
DEFGHIJKLMN
O
P
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
102430.999999999999998
0002.00000000006961
0
000000310
000
Minimum to
Start the
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
=WorkersHired
Next Year
=C15+C14-WorkersFired
=D15+D14-WorkersFired
=E15+E14-WorkersFired
=F15+F14-WorkersFired
=G15+G14-WorkersFired
=H15+H14-WorkersFired
=I15+I14-WorkersFired
=J15+J14-WorkersFired
=K15+K14-WorkersFired
=L15+L14-WorkersFired
=M15+M14-WorkersFired
>=
12
Labor Hours Available =SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWorker,C14:C15) =SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWor
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWo
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedWo
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedW
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrainedW
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrained
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTraine
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrain
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTrain
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTra
=SUMPRODUCT(LaborHoursPerTrainee:LaborHoursPerTra
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
Required Labor Hours 1600
2000
2000
2000
2800
3200
3600
3200
1600
1200
800
800
Labor Cost (Trainees) =LaborMonthlyWage*Trainees
Labor Cost (Trained Workforce) =LaborMonthlyWage*TrainedEmployees
Hiring Cost =HiringCost*WorkersHired
Severance Pay =SeverancePay*WorkersFired
Total Cost =SUM(C22:C25)
Total
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=LaborMonthlyWage*Trainees
=SUM(C22:N22)
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=LaborMonthlyWage*TrainedEmployees
=SUM(C23:N23)
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=HiringCost*WorkersHired
=SUM(C24:N24)
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SeverancePay*WorkersFired
=SUM(C25:N25)
=SUM(D22:D25)
=SUM(E22:E25)
=SUM(F22:F25)
=SUM(G22:G25)
=SUM(H22:H25)
=SUM(I22:I25)
=SUM(J22:J25)
=SUM(K22:K25)
=SUM(L22:L25)
=SUM(M22:M25)
=SUM(N22:N25)
=SUM(C26:N26)
Thus, WorkersHired (C11:N11) shows the number of workers Cool Power should hire each
month and WorkersFired (C12:N12) shows the number of workers Cool Power should fire each
month so as to achieve the minimum TotalCost (O26) of $787,500.
8