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 19 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. (a) Find the range of values that Resource 2 (labor-hours) can assume. x sbs 19 (b) For the current optimal solution to hold, constraint 3 (production of model A grates) cannot be decreased by more than 104 x grates per day.
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 19 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. (a) Find the range of values that Resource 2 (labor-hours) can assume. x sbs 19 (b) For the current optimal solution to hold, constraint 3 (production of model A grates) cannot be decreased by more than 104 x grates per day.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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![**Problem Statement:**
Kane Manufacturing has a division that produces two models of grates, model A and model B. The production details for each model are as follows:
- Model A grate requires 3 pounds of cast iron and 6 minutes of labor.
- Model B grate requires 4 pounds of cast iron and 3 minutes of labor.
**Profit Information:**
- Profit for each model A grate: $2.25
- Profit for each model B grate: $1.75
**Available Resources per Day:**
- Cast Iron: 1000 pounds
- Labor: 19 labor-hours
Due to excess inventory of model A grates, the management has decided to limit the production of model A grates to no more than 180 grates per day.
**Questions:**
(a) Find the range of values that Resource 2 (labor-hours) can assume.
\[ 0 \leq b \leq 19 \]
(b) For the current optimal solution to hold, constraint 3 (production of model A grates) cannot be decreased by more than:
\[ 104 \] grates per day.
**Graph and Diagram Information:**
_No graphs or diagrams are provided in the given image._](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c4f1739-57e2-4399-a976-93f96ef5c2b4%2F746f2407-3067-422f-b96c-a7aaf038db3a%2Fmw1vlaa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Kane Manufacturing has a division that produces two models of grates, model A and model B. The production details for each model are as follows:
- Model A grate requires 3 pounds of cast iron and 6 minutes of labor.
- Model B grate requires 4 pounds of cast iron and 3 minutes of labor.
**Profit Information:**
- Profit for each model A grate: $2.25
- Profit for each model B grate: $1.75
**Available Resources per Day:**
- Cast Iron: 1000 pounds
- Labor: 19 labor-hours
Due to excess inventory of model A grates, the management has decided to limit the production of model A grates to no more than 180 grates per day.
**Questions:**
(a) Find the range of values that Resource 2 (labor-hours) can assume.
\[ 0 \leq b \leq 19 \]
(b) For the current optimal solution to hold, constraint 3 (production of model A grates) cannot be decreased by more than:
\[ 104 \] grates per day.
**Graph and Diagram Information:**
_No graphs or diagrams are provided in the given image._
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