A company manufactures two products, A and B. The unit revenues are d $3, respectively. Two raw materials, M1 and M2, used in the facture of the two products have daily availabilities of 8 and 18 units, ctively. One unit of A uses 3 units of M1 and 2 units of M2, and 1 unit of s 2 units of M1 and 6 units of M2. a. Determine the dual prices of M1 and M2 and their feasibility ranges.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.5: Facility Location Models
Problem 24P
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3-63. 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 3 units of M1 and 2 units of M2, and 1 unit of
B uses 2 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.
*Dual price is another name for shadow price.
Transcribed Image Text:3-63. 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 3 units of M1 and 2 units of M2, and 1 unit of B uses 2 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. *Dual price is another name for shadow price.
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