A plant in the developing country can manufacture five different products in any combination. Each product needs time on each of these machines, as shown in table below. All figures are in minutes per pound of product.
|
|
Machine-Time (min/lb)
|
|
Product
|
1
|
2
|
3
|
|
A
|
12
|
8
|
5
|
|
B
|
7
|
9
|
10
|
|
C
|
8
|
4
|
7
|
|
D
|
10
|
0
|
3
|
|
E
|
7
|
11
|
2
|
Each machine is available 128 hours for each week. Products A, B, C, D, and E are purely competitive, and any amounts made might be sold at per pound prices of $5, $4, $5, $4 and $4 respectively. Variable labor costs are $4 for each hour for machine 1 and 2, and $3 per hour for machine 3. Material costs are $2 for each pound of products A and C, and $1 for each pound of products B, D and E. The management wants to maximize profit to the firm. The solver LP solution and sensitivity.
a) What is the Excel formula in B9 providing the first value of coefficient in the objective function?
b) How many hours are spent on each of three machines and what are the units of shadow prices on the constraints which control machine capacity?
c) How much should firm be willing to spend to obtain another hour of time on machine 2?
d) How much can the sales price of product A raise before optimal production changes?
State your answer in proper units