Question

1. A company manufactures two products, A and B. The unit revenues are $2 and $3, respectively. Two raw materials, M1 and M2, used in the manufacture of the two products have daily availabilities of 8 and 18 units, respectively. One unit of A uses 2 units of M1 and Aunits of M2, and 1 unit of B uses@ units of M1 and 6 units of M2 (a) Determine the dual prices of M1 and M2 and their feasibility ranges. (b) Suppose that 4 additional units of M1 can be acquired at the cost of 30 cents per unit. Would you recommend the additional purchase? (c) What is the most the company should pay per unit of M2? (d) If M2 availability is increased by 5 units, determine the associated optimum revenue.

Can i have the complete solution for this?

if needed using excel solver and the explanaition.

thank you!!!

Answer 1

Part (a):

To determine: Dual prices of M1 and M2 and their feasibility ranges

Solution:

The feasibility range of M1 is obtained as follows:

(6.0)→2(6)+2(0)=12:(0,3) ► 2(0)+2(3)=6;639, 512

The dual price of M1 is computed as follows:

Dual price of M1-(12-9) (12-6) = $0.50

Therefore, the feasibility range of M1 and its dual price is 6 ≤ q₁ ≤ 12 and $0.50, respectively.

The feasibility range of M2 is obtained as follows:

(4,0) +3(4) +6(0)=12:(0,4) +3(0) +6(4)=6:12 59, 524

The dual price of M2 is computed as follows:

Dual price of M2 (24-12) = $0.33

Therefore, the feasibility range of M2 and its dual price is 12 ≤ q₂ ≤ 24 and $0.33, respectively.

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Part (b):

Yes, it would be recommended to make the additional purchase if 4 additional units of M1 can be purchased at a cost of 30 cents per unit, as 8 and 4 would give 12 which is still in the range and $0.30 would be less than $0.50.

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Part (c):

The most the company needs to pay per unit of M2 would be the dual price of M2. The dual price of M2 is calculated below:

(12-8) Dual price of M2= (24-12) = $0.33

Therefore, the most the company needs to pay per unit of M2 is $0.33.

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Part (d):

To determine: Associated optimum revenue

Solution: Calculate the optimum revenue.

Optimum revenue = $10+5(0.33) = $11.65

Therefore, if M2 availability is increased by 5 more units, the associated optimum revenue would be $11.65.