A company manufactures two products A and B. The unit revenues are $(8) and $(10
ID: 343649 • Letter: A
Question
A company manufactures two products A and B. The unit revenues are $(8) and $(10) respectively. Two raw materials (M1 and M2) used in manufacture of the two products have daily availabilities of (12) and (21) units respectively. One unit of A uses 2 units of M1 and 2 units of M2, and 1 unit of B uses 3 units of M1 and 6 units of M2.
a)Determine the shadow prices of M1 and M2
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)If M2 availability is increased by 5 units, determine the associated optimum revenued) What is the most the company should pay per unit of M2
Explanation / Answer
Lets list out the inputs:
Revenue of A: $8
Revenue of B: $10
Availability of M1: 12 per day
Availability of M2: 21 per day
Production of A = 2*units of M1 + 2* units of M2
Production of B = 3*units of M1 + 6* units of M2
Total Revenue on A and B is = 8* units of A + 10* units of B
Per day production equations:
Number of units of M1 required for A and B is
2*units of M1(A) + 3*units of M1(B)<=12
Number of units of M2 required for A and B is
2*units of M2(A) + 6*units of M2(B)<=21
Units of M1 and Units of M2 cannot be 0
With the help of above 4 constraints:
Let’s find the range
(6,0)
à2*6+3*0
à12
(0,3)
à2*0+3*3
à9
M1 Range: 9<= units of M1 <=12
Dual price of M1 = (12-9)/(12-6) = $0.50
(4,0)
à 2(4) + 6(0) = 8
(0,4)
à 2(0) + 6(4) = 24;
M2 Range: 8 <=units of M2 <= 24;
Dual price of M2 = (12-8)/(24-12) = $0.33
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