You are given a linear programming problem. Maximize P = 3.5x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
You are given a linear programming problem. Maximize P = 3.5x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1 constraint 2 constraint 3
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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Question
You are given a linear programming problem.
| Maximize | P = 3.5x + 3y |
| subject to | 5x | + | 3y | ≤ | 30 | Resource 1 | |
| 2x | + | 3y | ≤ | 21 | Resource 2 | ||
| x | ≤ | 4 | Resource 3 | ||||
| y | ≥ | 0 | |||||
| x | ≥ | 0 |
(a) Use the method of corners to solve the problem.
(c) Find the range of values that Resource 1 can assume.
(d) Find the shadow price for Resource 1.
(e) Identify the binding and nonbinding constraints.
The maximum is P = at
(b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.(x, y) =
.
≤ c ≤
(c) Find the range of values that Resource 1 can assume.
≤ (Resource 1) ≤
(d) Find the shadow price for Resource 1.
(e) Identify the binding and nonbinding constraints.
| constraint 1 | ||
| constraint 2 | ||
| constraint 3 |
Expert Solution
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Find the feasible region by plotting the constraints
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