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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? TATL con

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? TATL con

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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Step 1: a) Determining the dual prices and feasibility ranges. Formulate the Linear Programming Problem (LPP) - Primal Problem Maximize Z = 2x₁ + 3x₂ Subject to the constraints: 3x₁ + 2x₂ <8 (Raw material M1 constraint) 2x₁ + 6x₂ < 18 (Raw material M2 constraint) X₁ 20 X₂ ≥ 0 Solve the Primal Problem Solving this primal problem (using a solver or graphical method), we find the optimal solution: x₁ = 2; x₂ = 2 Maximum Revenue (Z) = $ 10 Formulate the Dual Problem Objective Function: Minimize W = 8y₁ + 18y/2 Subject to the constraints: 3y₁ + 2y₂ ≥ 2 2y₁ + 6y₂ ≥ 3 Y₁ 20 Y₂ ≥ 0
Transcribed Image Text:Step 1: a) Determining the dual prices and feasibility ranges. Formulate the Linear Programming Problem (LPP) - Primal Problem Maximize Z = 2x₁ + 3x₂ Subject to the constraints: 3x₁ + 2x₂ <8 (Raw material M1 constraint) 2x₁ + 6x₂ < 18 (Raw material M2 constraint) X₁ 20 X₂ ≥ 0 Solve the Primal Problem Solving this primal problem (using a solver or graphical method), we find the optimal solution: x₁ = 2; x₂ = 2 Maximum Revenue (Z) = $ 10 Formulate the Dual Problem Objective Function: Minimize W = 8y₁ + 18y/2 Subject to the constraints: 3y₁ + 2y₂ ≥ 2 2y₁ + 6y₂ ≥ 3 Y₁ 20 Y₂ ≥ 0
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