= 2x + 1.5y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0
= 2x + 1.5y subject to 3x + 4y ≤ 1000 Resource 1 6x + 3y ≤ 1200 Resource 2 x ≤ 180 Resource 3 y ≥ 0 x ≥ 0
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
Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day.
| Maximize | P = 2x + 1.5y |
| subject to | 3x | + | 4y | ≤ | 1000 | Resource 1 | |
| 6x | + | 3y | ≤ | 1200 | Resource 2 | ||
| x | ≤ | 180 | Resource 3 | ||||
| y | ≥ | 0 | |||||
| x | ≥ | 0 |
(a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)
$
(b) Identify the binding and nonbinding constraints.
$
(b) Identify the binding and nonbinding constraints.
| constraint 1 | ||
| constraint 2 | ||
| constraint 3 |
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