Question

3 Gepbab Production Company uses labor and raw material to produce three products. The resource requirements and sales price for the three products are as shown in Table 10. Currently, 60 units of raw material are available. Up to 90 hours of labor can be purchased at Sl per hour. To maximize Gepbab profits, solve the following LP: max z = 6X1 + 8X2 + 13X3 - L s.t. 3X1 + 4X2 + 6X3 - LS 0 2X1 + 2X2 + 5x3 = 60 Ls 90 X1, X2, X3, L 20 Here, X; = units of product i produced, and L = number of labor hours purchased. Use the LINDO output in Figure 21 to answer the following questions: a What is the most the company should pay for an- other unit of raw material? b What is the most the company should pay for an- other hour of labor? C What would product 1 have to sell for to make it de- sirable for the company to produce it? d If 100 hours of labor could be purchased, what would the company's profit be? e Find the new optimal solution if product 3 sold for $15. TABLE 10 Product Resource 1 2 Labor (hours) Raw material (units) Sales price (S) 2 25 6 8 13

Answer 1

a)

Shadow price/ dual price of raw material constraint is $0.5 so another unit of raw material will increase profit by $0.5 so company can only pay $0.5 at most for another unit of raw material

b)

Shadow price/ dual price of Labour hours constraint is $0.75 so another unit of labour hours will increase profit by $0.75 so company can only pay $0.75 at most for another unit of labour hours

c)
Correct answer is $6.25

With reduced cost of 0.25 Product 1 needs to be sold at least $6.25 (Present 6 + reduced cost 0.25) to balance

d)

100 units of labour hours will increase profit by 100*0.75 = 7.5 so new profit would be 97.5+7.5 = 105

e)

Optimal solution will remain same as increase to $15 from present $13 is within allowable increase limit