CASE I: PRODUCT MIX
Geena is the Production manager of Clear Shampoo and she wants to
determine the production mix that will result in maximum profit. She is able to
determine the data necessary for her to make a decision. It will take 5 minutes to
mix 1 case of Men’s shampoo and 10 minutes to mix 1 case of Women’s shampoo
and she has a total of 100 minutes available for the mixing process per day. It will
take 7 minutes to bottle 1 case of Men’s Shampoo and 7 minutes to bottle 1 case of
Women’s shampoo and she has a total of 84 minutes available for the bottling
process per day. It will take 9 minutes to pack 1 case of Men’s shampoo and 5
minutes to pack 1 case of Women’s shampoo and she has a total of 90 minutes
available for the packing process per day. She will earn $6 for every case of Men’s
shampoo produced and $8 for every case of Women’s shampoo produced.
Perform an analysis for Clear shampoo in order to determine how many
cases of Men’s Shampoo and Women’s shampoo should be produced per day to
maximize profits. Prepare a report presenting the objectives, best possible
solutions and recommendations. Include (but do not limit your discussion to) a
consideration of the following:
1. The recommendation number of units to produce to maximize the total
contribution to profit for an 8 hour shift. What reason might management
have for not implementing your recommendation?
2. Suppose the management also states that the number of Men's Shampoo
produced must be at least as great as the number of Women's Shampoo
produced. Assuming that the objective is to maximize the total contribution
to profit for an 8 hour shift, how many units of each shampoo should be
produced?
For each solution that you develop, include a copy of your linear programming
model and graphical solution to your report.
LINEAR PROGRAMMING
Man (X)
Woman (Y)
TOTAL
MIXING
5
10
100
BOTTLING
7
7
84
PACKING
9
5
90
PROFIT
$6
$8
???
Max = 6x + 8y
5x + 10y ≤ 100
7x + 7y ≤ 84
9x + 5y ≤ 90
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
I.
5y = 90
5x + 10y ≤ 100
5
X=0
5
Y = 18
5 (0) + 10y = 100
10y = 100
10
Y=0
10
9x + 5 (0) = 90
Y = 10
9x = 90
9
Y=0
9
X = 10
5x + 10 (0) = 100
5x = 100
5
5
I
II
III
X
20
12
10
Y
10
12
18
X = 20
II.
7x + 7y = 84
X=0
7 (0) + 7y = 84
7y = 84
7
7
Y = 12
X = 12
III.
9x + 5y = 90
X=0
9 (0) + 5y = 90
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
Constraint I
Constraint II
Constraint III
(5x + 10y ≤ 100) * 14
(7x + 7y ≤ 84) * 9
(5x + 10y ≤ 100) / -2
(7x + 7y ≤ 84) * -10
(9x + 5y ≤ 90) * -7
9x + 5y ≤ 90
70x + 140y ≤ 1400
63x + 63y ≤ 756
-2.5x -5y ≤ -50
-70x -70y ≤ -840
-63x -35y ≤ -630
9x + 5y ≤ 90
70y ≤ 560
28y = 126
6.5x = 40
70
28
6.5
70
28
6.5
Y=8
Y = 4.5
X = 6.15
5x + 10y ≤ 100
7x + 7y ≤ 84
5x + 10y ≤ 100
5x + 10 (8) = 100
7x + 7 (4.5) = 84
5 (6.15) + 10y= 100
5x + 80 = 100
7x + 31.5 = 84
30.75 + 10y = 100
5x = 20
7x = 52.5
10y = 69.25
5
5
X=4
Constraint I.
Constraint II.
Constraint III.
7
7
X = 7.5
X
4
7.5
6.15
10
10
X = 6.93
Y
8
4.5
6.93
5x + 10y ≤ 100
7x + 7y ≤ 84
9x + 5y ≤ 90
21x + 22y = 274
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
I.
I.
21 (4) + 22 (8) = 274
5 (7.5) + 10 (4.5) ≤ 100
84 + 176 = 274
37.5 + 45 = 100
260 = 274
82.5 = 100
II.
II.
21 (7.5) + 22(4.5) = 274
7 (7.5) + 7 (4.5) ≤ 84
157.5 + 99 = 274
52.5 + 31.5 = 84
265.5 = 274
84 = 84
III.
III.
21 (6.15) + 22 (6.93) = 274
9 (7.5) + 5 (4.5) ≤ 90
129.15 + 152.46 = 274
67.5 + 22.5 = 90
281.61 = 274
90 = 90
Max = 6x + 8y
CASE II: SUPPLY MIX
Raul is the Production Analyst of Dole Pineapple and he wants to determine
the supply mix that will result to minimum cost. He is able to determine the data
necessary for him to make a decision. A barrel of Absolute water can produce 9
cases of sliced pineapple, 8 cases of pineapple chunks and 4 cases of crushed
pineapple. A barrel of Wilkins water can produced 5 cases of sliced of pineapple, 8
cases of pineapple chunks, and 11 cases of crushed pineapple. Lester must
produce at least 90 cases of sliced pineapple, 128 pineapple chunks, and 88 cases
of crushed pineapple per day. Absolute water costs $20 per barrel while Wilkins
water costs $22 per barrel.
Analyse the production problem of Dole Pineapple in order to determine how many
barrels of Absolute and Wilkins should be purchase per day to minimize cost.
Prepare a report presenting the objectives best possible solutions and
recommendations. Include (but do not limit your discussion to) a consideration of
the following:
1. What is the recommended number of sliced pineapple, crushed pineapple
and pineapple chunks to produce in order to maximize profit? (Retail
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
price of sliced pineapple per case: $50, crushed pineapple per case is $60
and a pineapple chunk per case is $55.
2. Where efforts should be expended in order to increase profits?
For each solution that you develop, include a copy of your linear programming
model and graphical solution to your report.
Absolute (X)
Wilkins (Y)
Demand
Retail price
per sliced
SLICED
PINEAPPLE
9 cases
5 cases
90 cases
$50
PINEAPPLE
CHUNKS
8 cases
8 cases
128 cases
$60
CRUSHED
PINEAPPLE
4 cases
11 cases
88 cases
$55
COST
$20
$22
???
CASE III. PRODUCT MIX 2
Lander is the plant manager of Converse and he wants to determine the
product mix that will result in maximum profit. He is able to determine the data
necessary for him to make a decision. It will take 14 minutes to cut 1 unit of Chuck
and 16 minutes to cut 1 unit of Jack and he has to use up at least 224 minutes of
subcontracted cutting process per day. It will take 18 minutes to sew 1 unit of
Chuck and 8 minutes to sew 1 unit of Jack and he has to use up at least 144
minutes of subcontracted sewing process per day. It will take 10 minutes to adhere
1 unit Chuck and 20 minutes to adhere 1 unit of Jack and he has to use up at least
200 minutes of subcontracted process per day. He will earn $24 for every unit of
Chuck produced and $29 for every unit of Jack produced.
Perform an analysis for Converse in order to determine how many units of
Chuck and Jack should be produced per day to maximize profits. Prepare a report
presenting the objectives, best possible solutions and recommendations. Include
(but do not limit your discussion to) a consideration of the following:
1. The recommendation number of units to produce to maximize the total
contribution to profit for a 12 hour shift. What reason might management have for
not implementing your recommendation?
2. Suppose the management also states that the number of Chuck produced
must be at least as great as the number of Jack produced. Assuming that the
objective is to maximize the total contribution to profit for a 12 hour shift, how
many units of each shoes should be produced?
For each solution that you develop, include a copy of your linear
programming model and graphical solution to your report.
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
CASE IV. PRODUCT MIX 4
Lovely is the plant manager of Acer Inc., and she wants to determine the
product mix that will result in maximum profit. She is able to determine the data
necessary for her to make a decision. It will take 20 minutes to fabricate 1 unit of
Aspire and 12 minutes to fabricate 1 unit of Extensa and she has to use at least 240
minutes of the subcontracted fabrication process per day. It will take 16 minutes
to assemble 1 unit of Aspire and 18 minutes to assemble 1 unit of Extensa and she
has to use up at least 288 minutes of the subcontracted assembly process per day.
It will take 6 minutes to test 1 unit of Aspire and 22 minutes to test 1 unit of
Extensa and she has to use up at least 132 minutes of the subcontracted testing
process per day. She will earn $6 for every unit of Aspire produced and $7 for
every unit of Extensa produced.
Perform an analysis for Acer Inc. in order to determine how many units of
Aspire and Extensa should be produced per day to maximize profits. Prepare a
report presenting the objectives, best possible solutions and recommendations.
Include (but do not limit your discussion to) a consideration of the following:
1. The recommendation number of units to produce to maximize the total
contribution to profit for an 8 hour shift. What reason might management have for
not implementing your recommendation?
2. Suppose the management also states that the number of Aspire produced
must be at least as great as the number of Extensa produced. Assuming that the
objective is to maximize the total contribution to profit for an 8 hour shift, how
many units of each computer should be produced?
For each solution that you develop, include a copy of your linear
programming model and graphical solution to your report.
CASE V. TRANSPORT SOLUTION
Charles is the Vice President for Europe of Colgate's Palmolive Shampoo. He
supervises three factories (Madrid, Moscow and Athens) that supply three
warehouses (London, Berlin and Paris) in the region. Madrid can produce 500 cases,
Moscow can produce 300 cases and Athens can produce up to 100 cases per week.
Meanwhile, London's demand is 400 cases; Berlin's demand is 600 cases, and
Paris's demand is 200 cases per week. The shipping cost per case from Madrid to
London $8, to Berlin is $5, and to Paris is $7. The shipping cost per case from
Moscow to London is $3, to Berlin is $9, and to Paris is $11. The shipping cost per
case from Athens to London is $10, to Berlin is $6, and to Paris is $4.
Perform an analysis in order to determine how many cases will Charles ship
an of the three factories to each of the three warehouses in the region per week
while minimizing shipping costs. Prepare a report presenting the objectives, best
possible solutions and recommendations. Include (but do not limit your discussion
to) a consideration of the following:
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
1)
Over the next 5 years the demand growth of each product increases to 10%
yearly, would you recommend that Europe of Colgate's Palmolive Shampoo
consider plant expansion at this time?
2)
The Company wants to explore the possibility of satisfying some of the
customer demand directly from the production plant. What are your
recommendations to management to consider the direct plant to customer
shipments?
CASE VI. ASSIGNMENT MODEL
Faye is the Division Head of Standard Chartered for North Africa. Three
branches were just opened and she has to assign one Branch manager for each of
the branches. She has shortlisted four candidates for the new positions and has to
assign them based on minimum cost possible. The cost of assigning a manager to
each of the three branches is determined. It will cost $11,000 to assign Irwin to
Cairo, $20,000 to Dubai, and $15,000 to Algiers. It will cost $12,000 to assign Janet
to Cairo, $13,000 to Dubai and $21,000 to Algiers. It will cost $18,000 to assign
Karlo to Cairo, $14,000 to Dubai, and $22,000 to Algiers. It will cost $19,000 to
assign Liza to Cairo, $17,000 to Dubai, and $16,000 to Algiers.
Perform an analysis in order to determine which manager Faye should assign
to what location. Prepare a report presenting the objectives, best possible solutions
and recommendations. Include but do not limit your discussion to) a consideration
of the following.
1) In case one of the assigned managers resigned from his/her post, what are
your recommendations to management in replacing the resigned manager?
2) Each manager will be provided an annual increase of 10%, Would you
recommend a new assignment for each manager?
CASE VII. NETWORK MODEL
Kenneth is the Capacity Planner of Manila waters and he is tasked to ensure
the maximum amount of water flows from Water Pump A to Water Pump G. He has
able to determine the capacity of the outflow and inflow of water from one pump
to another in liters per second. The capacity figures are summarized below:
Water Pump
From
To
A
B
A
D
B
C
B
E
C
D
C
E
Capacity (Liters / Second)
Out
In
6
1
4
5
5
8
7
4
3
9
2
0
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
D
E
E
F
F
F
G
G
1
0
8
9
7
6
2
3
Prepare a network design in order to determine the total capacity of the
water flow.
CASE VIII. MARKET SHARE
Izza is the Internal Vice President of BPI and she wants to know the
company's future market share compared to its competitors in the banking
industry. She was able to determine the present number of clients each major
player has at the start of the year and the movement of clients on a monthly basis
from one company to another. The figures are summarized below
No. of Clients
BPI
400
January
Next Month
From BPI
From BDO
From RCBC
Total
240
100
40
380
Savings Bank
BDO
500
To
50
210
10
330
Total
RCBC
100
110
130
50
290
1000
Total
400
500
100
1000
Perform an analysis in order to determine the company's market share in the
long run. Prepare a report presenting the objectives, best possible solutions and
recommendations. Include (but do not limit your discussion to) a consideration of
the following:
1) Provide a recommendation on how to increase market share based on
analysis performed,
2) Identify the company's future market share compared to its competitors in
the banking industry using Gauss-Jordan Method.
CASE IX. RECEIVABLE ACCOUNTS
John is the Finance Director of Home cable and he wants to know the
collection efficiency of the company. He was able to determine the actual
collection and aging schedule of accounts receivable for the month of January and
the month of February. The figures are summarized below:
Bills ($)
Status
Paid
Bad
<1
month
Total
1-3 month
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???
January
Next
Month
From Paid
From Bad
From <1
month
From 1-3
month
Total
400
200
300
100
1000
Total
To
400
0
150
0
200
0
0
0
50
0
0
100
400
200
300
50
30
0
20
100
600
230
50
120
1000
Perform an analysis in order to determine company’s actual paid and bad
debt. Prepare a report presenting the objectives, best possible solutions and
recommendations. Include (but do not limit your discussion to) a consideration of
the following:
1) Provide a collection strategy to minimize receivables default,
2) In case the actual payment in the end does not realize, do you recommend
to the management to record the uncollectible amount to bad debts?
CASE X. INVENTORY MODEL
Sonny, the Vice president of Longines Wristwatch wants to determine the
most optimum inventory practice for the company. He was able to determine the
demand and inventory costs needed in his analysis. The annual demand is 20,000
units. The cover set up of machinery for production is $40,000 per set up and the
holding cost is $500 per unit per year. The production rate is 100 units per day
and there are 250 working days per year.
Perform an analysis in order to determine company's economic order
quantity and production cycle. Prepare a report presenting the objectives, best
possible solutions and recommendations. Include (but do not limit your discussion
to) consideration of the following:
1) Assuming the production rate increases from 100 units per day to 120
units per day, what is the new economic order point?
2) Assume the annual demand increases to 20%, with the same scenario
above, what is your management recommendation to identify the total
inventory cost?
Management Science / BSA II / 2nd Semester AY 2019 – 2020 / Page 2 of ???