Answered: Maximize P = 1.5x + 1y subject to…

Name: Kane Manufacturing has a division that produces two models of grates,
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: 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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

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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 $1.50, and the profit for each model B grate is $1.00. 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 = 1.5x + 1y

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.

constraint 1		---Select--- binding nonbinding
constraint 2		---Select--- binding nonbinding
constraint 3		---Select--- binding nonbinding

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