Consider the following model. Maximize subject to x₂ + x₂ x1 x₂ + x3 Z = 4x₁ + 8x₂ + 10x3 + 6x4 x3 + x4 X3 +x5 +x6 - 2x5 ≤ 320 ≤ 320 +x7+x8 ≤ 320 ≤ 120 ≤ 120 ≤ 120 - 2x8 ≤ 120 +x6+x7 -2x6 - 2x7 (constraint 1/resource 1) (constraint 2 / resource 2) (constraint 3/resource 3) (constraint 4 / resource 4) (constraint 5/resource 5) (constraint 6 / resource 6) (constraint 7 / resource 7) X4 and x; ≥ 0, j = 1, 2, ..., 8. (a) Make up a story that has this linear programming model. (b) Use Excel Solver to find the optimal solution. (c) Identify which constraint is binding. (d) Use Excel Solver to find shadow price for each resource. (Do not use ASPE's solver, which was not covered in lecture anyway) (e) Use the simplex method in tabular form to find the optimal solution step by step. Because this involves many iterations (about 8 iterations), I am giving you the simplex tableau after the 4th iteration for your reference. If there are multiple rows with the same minimum ratio, let's choose the first min ratio row, that way we should all end up with the same tableau after each iteration. For example, if Eq2 row and Eq3 row both have the same minimum ratio, we choose Eq2 row as the pivot row. (f) Use the last tableau of the simplex method to read shadow price for each resource.
Consider the following model. Maximize subject to x₂ + x₂ x1 x₂ + x3 Z = 4x₁ + 8x₂ + 10x3 + 6x4 x3 + x4 X3 +x5 +x6 - 2x5 ≤ 320 ≤ 320 +x7+x8 ≤ 320 ≤ 120 ≤ 120 ≤ 120 - 2x8 ≤ 120 +x6+x7 -2x6 - 2x7 (constraint 1/resource 1) (constraint 2 / resource 2) (constraint 3/resource 3) (constraint 4 / resource 4) (constraint 5/resource 5) (constraint 6 / resource 6) (constraint 7 / resource 7) X4 and x; ≥ 0, j = 1, 2, ..., 8. (a) Make up a story that has this linear programming model. (b) Use Excel Solver to find the optimal solution. (c) Identify which constraint is binding. (d) Use Excel Solver to find shadow price for each resource. (Do not use ASPE's solver, which was not covered in lecture anyway) (e) Use the simplex method in tabular form to find the optimal solution step by step. Because this involves many iterations (about 8 iterations), I am giving you the simplex tableau after the 4th iteration for your reference. If there are multiple rows with the same minimum ratio, let's choose the first min ratio row, that way we should all end up with the same tableau after each iteration. For example, if Eq2 row and Eq3 row both have the same minimum ratio, we choose Eq2 row as the pivot row. (f) Use the last tableau of the simplex method to read shadow price for each resource.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:Consider the following model.
Maximize
subject to
x₁ + x₂
X1
x₂ + x3
x2
Z = 4x₁ + 8x₂ + 10x3 + 6x4
x3 + x4
X3
+x5+x6
- 2x5
< 320
≤ 320
+x7+x8 ≤ 320
≤ 120
≤ 120
< 120
- 2xg ≤ 120
+x6 +x7
- 2x6
- 2x7
(constraint 1 / resource 1)
(constraint 2 / resource 2)
(constraint 3 / resource 3)
(constraint 4 / resource 4)
(constraint 5/resource 5)
(constraint 6 / resource 6)
(constraint 7 / resource 7)
X4
and x; ≥ 0, j = 1, 2, ..., 8.
(a) Make up a story that has this linear programming model.
(b) Use Excel Solver to find the optimal solution.
(c) Identify which constraint is binding.
(d) Use Excel Solver to find shadow price for each resource. (Do not use ASPE's solver, which was
not covered in lecture anyway)
(e) Use the simplex method in tabular form to find the optimal solution step by step.
Because this involves many iterations (about 8 iterations), I am giving you the simplex tableau after the
4th iteration for your reference. If there are multiple rows with the same minimum ratio, let's choose the
first min ratio row, that way we should all end up with the same tableau after each iteration. For
example, if Eq2 row and Eq3 row both have the same minimum ratio, we choose Eq2 row as the pivot
row.
(f) Use the last tableau of the simplex method to read shadow price for each resource.
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