Max 3x1 + 2x2 s.t. 1x1 + 1x2 ≤ 10 3x1 + 1x2 < 24 1x1 + 2x2 ≤ 16 And x1, x2 > 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of x1, x2, and Z. b) Assume that the objective function coefficient for x1 changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective function coefficient for x2 changes from 2 to 4. Does the optimal solution change? d) What are the shadow prices for these constraints? e) What conclusions can you draw about changes to the right hand side of constraint 2? f) Identify the binding and non-binding constraints in this problem and explain.
Max 3x1 + 2x2 s.t. 1x1 + 1x2 ≤ 10 3x1 + 1x2 < 24 1x1 + 2x2 ≤ 16 And x1, x2 > 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of x1, x2, and Z. b) Assume that the objective function coefficient for x1 changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective function coefficient for x2 changes from 2 to 4. Does the optimal solution change? d) What are the shadow prices for these constraints? e) What conclusions can you draw about changes to the right hand side of constraint 2? f) Identify the binding and non-binding constraints in this problem and explain.
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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Transcribed Image Text:1. Consider the following linear program
Max 3x1 + 2x2
s.t.
1x1 + 1x2 ≤ 10
3x1 + 1x2 <24
1x1 + 2x2 ≤ 16
And x1, x2 > 0.
a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of
x1, x2, and Z.
b) Assume that the objective function coefficient for x1 changes from 3 to 5. Does the
optimal solution change?
c) Assume that the objective function coefficient for x1 remains 3, but the objective
function coefficient for x2 changes from 2 to 4. Does the optimal solution change?
d) What are the shadow prices for these constraints?
e) What conclusions can you draw about changes to the right hand side of constraint 2?
f) Identify the binding and non-binding constraints in this problem and explain.
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