a. Write the dual problem b. State the value of each dual variable. c. State the...
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a. Write the dual problem b. State the value of each dual variable. c. State the value of the dual objective function. d. Verify that total contribution is the sum of the contributions of the individual resources. e. Determine how much the price of x2 would have to increase before this process became profitable. f. Would we utilize a proposed new process that has a profit contribution of $2 and consumes 1 unit of each productive resource? Would we utilize the process if it has a profit contribution of .95 and used 1 unit of the first and third resources only? 12. Max Z = 2x1 + 1x2 + 2.5X3 s.t. 0 Row I II III NC 2x1 + 2x2 + 3x3 ≤ 29 4x1 + 1x2 + 1x3 ≤ 20 2x1 + 2x2 + 2x3 ≤ 20 X1, X2, X3 ≥ 0 Price Vector 2.5 0 2 Solution Vector X3 S₂ X1 -Z Quantity Vector 776 9 1 -24.50 (labor) (machine time) (raw material) ZOOLO 2 X1 0 0 1 0 12031 X2 -3 -1 2.5 X3 HOOO 1 0 ܘ ܟ ܝ ܚܝ ܝܕ 0 S1 0 -1 -1/2 OOLOO 0 S2 0 1 0 0 0 S3 -1 -5 3/2 -1/2 a. Write the dual problem b. State the value of each dual variable. c. State the value of the dual objective function. d. Verify that total contribution is the sum of the contributions of the individual resources. e. Determine how much the price of x2 would have to increase before this process became profitable. f. Would we utilize a proposed new process that has a profit contribution of $2 and consumes 1 unit of each productive resource? Would we utilize the process if it has a profit contribution of .95 and used 1 unit of the first and third resources only? 12. Max Z = 2x1 + 1x2 + 2.5X3 s.t. 0 Row I II III NC 2x1 + 2x2 + 3x3 ≤ 29 4x1 + 1x2 + 1x3 ≤ 20 2x1 + 2x2 + 2x3 ≤ 20 X1, X2, X3 ≥ 0 Price Vector 2.5 0 2 Solution Vector X3 S₂ X1 -Z Quantity Vector 776 9 1 -24.50 (labor) (machine time) (raw material) ZOOLO 2 X1 0 0 1 0 12031 X2 -3 -1 2.5 X3 HOOO 1 0 ܘ ܟ ܝ ܚܝ ܝܕ 0 S1 0 -1 -1/2 OOLOO 0 S2 0 1 0 0 0 S3 -1 -5 3/2 -1/2
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a The dual problem for the given linear programming problem is as follows Minimize W 29y 20y 20y sub... View the full answer
Related Book For
Basic Technical Mathematics
ISBN: 9780137529896
12th Edition
Authors: Allyn J. Washington, Richard Evans
Posted Date:
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