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 $2.25, and the profit for each model B grate is $1.75. 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 subject to P = 2.25x + 1.75y 3x + 4y ≤ 1000 6x + 3y ≤1200 x 180 yz 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.) $ Resource 1 Resource 2 Resource 3 (b) Identify the binding and nonbinding constraints. -Select- v constraint 1 constraint 2 constraint 3 -Select-v ---Select---
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 $2.25, and the profit for each model B grate is $1.75. 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 subject to P = 2.25x + 1.75y 3x + 4y ≤ 1000 6x + 3y ≤1200 x 180 yz 0 x ≥ 0 (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.) $ Resource 1 Resource 2 Resource 3 (b) Identify the binding and nonbinding constraints. -Select- v constraint 1 constraint 2 constraint 3 -Select-v ---Select---
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 54P
Related questions
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 $2.25, and the profit for each model B grate is $1.75. 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
subject to
P = 2.25x + 1.75y
3x +
6x +
4y < 1000
3y ≤ 1200
X
180
y z
0
X > 0
Resource 1
Resource 2
Resource 3
(a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)
$
constraint 1
constraint 2
constraint 3
(b) Identify the binding and nonbinding constraints.
---Select--- ✓
---Select--- ✓
---Select--- V](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79cbc358-f9c7-4513-8a58-8a5e6560b01b%2Fb1e45960-18ee-481a-bf5d-bcd54d5fd1b0%2F1dpepbv_processed.png&w=3840&q=75)
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 $2.25, and the profit for each model B grate is $1.75. 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
subject to
P = 2.25x + 1.75y
3x +
6x +
4y < 1000
3y ≤ 1200
X
180
y z
0
X > 0
Resource 1
Resource 2
Resource 3
(a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)
$
constraint 1
constraint 2
constraint 3
(b) Identify the binding and nonbinding constraints.
---Select--- ✓
---Select--- ✓
---Select--- V
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