1- Mack’s guitar fabrication shop produces low cost, highly durable guitars for
beginners. Typically, out of the 100 guitars that begin production each month, only 80
percent are considered good enough to sell. The other 20 percent are scrapped due to
quality problems that are identified after they have completed the production process.
Each guitar sells for $250. Because some of the production process is automated, each
guitar only requires 10 labor hours. Each employee works an average of 160 hours per
month. Labor is paid at $10/hour, materials cost is $40/guitar, and overhead is $4,000.
a) Calculate the labor and multifactor productivity ratio.
b) After some study, the operations manager recommends 3 options to improve the
company’s multifactor productivity: (1) increase the sales price by 10 percent, (2)
improve quality so that only 10 percent are defective, or (3) reduce labor, material,
and overhead costs by 10 percent. Which option has the greatest impact on the
multifactor productivity measure?
Calculate the labor and multifactor productivity ratio.
100/160=0,625
(250*80) / [(160*10)+(40*100)+4000] = 20000/9600=2,08
After some study, the operations manager recommends 3 options to improve the company’s
multifactor productivity: (1) increase the sales price by 10 percent, (2) improve quality so that only 10
percent are defective, or (3) reduce labor, material, and overhead costs by 10 percent. Which option
has the greatest impact on the multifactor productivity measure?
1-250*0,10=25 new sales price=250+25=275
(275*80) / [(160*10)+(40*100)+4000] =2,29
2-(250*90) / [(160*10)+(40*100)+4000] =2,34
3-[(160*9)+(36*100)+3600] =8640 new total cost
(250*80) /8640 =2,31
Second option has the greatest impact on the multifactor productivity measure.
2- Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are
produced via two production processes: 1 and 2. Running process 1 for an hour costs
$4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1
and produces 1 unit of A and 1 of B.To meet customer demands, at least 10 units of A,
5 of B, and 3 of C must be produced daily. Graphically determine a daily production
plan that minimizes the cost of meeting Leary Chemical’s daily demands.
A
3
1
>=
10
PROCESS1
PROCESS2
PRODUCT
B
1
1
>=
5
C
1
>=
3
Min z= 4*x1 +1*x2
s.t
3x1+x2 >=10
x1+x2>=5
x1>=3
x1,x2 >=0
3x1+x2 =10
3x1+x2=10
x1=3,33 x2=0
x1=0 x2=10
x1+x2=5
x1=3
x1=5 x2=0
x1=0 x2=5
x1=3
for point A
x1+x2=5
x1=3
so
x1=3 x2=1
X2
10
5
2,5
A
2
1
B
2,5
3 3,5
5
A,B, points are feasible points.
A(3,2); B(5,0)
Minimum cost for point;
Z=4x1+x2
A(3,2); 4*3+2=14 (optimal point)
B(5,0); 4*5+0=20
X1
3- Jenny Lind is a writer of romance novels. A movie company and a TV network both
want exclusive rights to one of her more popular works. If she signs with the network,
she will receive a single lump sum, but if she signs with the movie company, the
amount she will receive depends on the market response to her movie. What should
she do?
Payouts and Probabilities
Movie company Payouts
Small box office - $200,000
Medium box office - $1,000,000
Large box office - $3,000,000
TV Network Payout
Flat rate - $900,000
Probabilities
P(Small Box Office) = 0.3
P(Medium Box Office) = 0.6
P(Large Box Office) = 0.1
4- A manufacturer with four production locations wishes to minimize the shipping cost to
their four warehouses. The supply from each factory and the demand of each
warehouse are shown in the table along with the cost to ship one unit from each
factory to each warehouse.
Factory
A
B
C
D
Total
Demand
Warehouse Warehouse Warehouse Warehouse Total
1
2
3
4
Supply
$5
$6
$4
$7
250
$8
$3
$7
$4
150
$6
$4
$5
$6
300
$7
$3
$4
$2
250
300
200
150
300
What is the lowest total cost for the factories to supply the warehouses with Northwest model and VAM ?
According to Vogel’s Approximation Model(VAM)
1.rule; find the difference between lowest two cost values in every columns and rows
2.rule;define the highest difference and choose the lowest cost in its column or row
3.rule begin with that cell