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 s1000 Resource 1 6x + 3y s1200 Resource 2 xS 180 Resource 3 y 2 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.) $ 40

Algebra for College Students
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Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
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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.
P = 1.5x + 1y
subject to 3x + 4y <1000
6x + 3y <1200
X < 180
y 2
Maximize
Resource 1
Resource 2
Resource 3
(a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)
$ 40
(b) Identify the binding and nonbinding constraints.
binding
constraint 1
constraint 2
binding
constraint 3
nonbinding v
Transcribed Image Text: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. P = 1.5x + 1y subject to 3x + 4y <1000 6x + 3y <1200 X < 180 y 2 Maximize Resource 1 Resource 2 Resource 3 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.) $ 40 (b) Identify the binding and nonbinding constraints. binding constraint 1 constraint 2 binding constraint 3 nonbinding v
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