Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $3.50, and the profit for each model B grate is $2.50. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit? (x, y) = ( 120, 160 What is the optimal profit? $ 820
Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $3.50, and the profit for each model B grate is $2.50. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit? (x, y) = ( 120, 160 What is the optimal profit? $ 820
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem Statement: Production Optimization for Kane Manufacturing**
Kane Manufacturing has a division that produces two models of fireplace grates: \(x\) units of model A and \(y\) units of model B.
- To produce each model A grate, it requires 3 lb of cast iron and 6 min of labor.
- To produce each model B grate, it requires 4 lb of cast iron and 3 min of labor.
- The profit for each model A grate is \$3.50, and the profit for each model B grate is \$2.50.
- Additionally, there are 1000 lb of cast iron and 20 labor-hours available for the production of fireplace grates per day.
Due to a backlog of orders for model A grates, Kane's manager has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
**Solution Attempt:**
\[
(x, y) = \left( \begin{array}{c}
120 \\
160 \end{array} \right) \times
\quad \textcolor{red}{\text{Incorrect}}
\]
**Question:**
What is the optimal profit?
**Answer Attempt:**
\[
\ \text{\$820} \quad \textcolor{red}{\text{Incorrect}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c4f1739-57e2-4399-a976-93f96ef5c2b4%2F0925770e-a151-48d0-b82e-75e63e024db4%2F3z2lx73_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Production Optimization for Kane Manufacturing**
Kane Manufacturing has a division that produces two models of fireplace grates: \(x\) units of model A and \(y\) units of model B.
- To produce each model A grate, it requires 3 lb of cast iron and 6 min of labor.
- To produce each model B grate, it requires 4 lb of cast iron and 3 min of labor.
- The profit for each model A grate is \$3.50, and the profit for each model B grate is \$2.50.
- Additionally, there are 1000 lb of cast iron and 20 labor-hours available for the production of fireplace grates per day.
Due to a backlog of orders for model A grates, Kane's manager has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
**Solution Attempt:**
\[
(x, y) = \left( \begin{array}{c}
120 \\
160 \end{array} \right) \times
\quad \textcolor{red}{\text{Incorrect}}
\]
**Question:**
What is the optimal profit?
**Answer Attempt:**
\[
\ \text{\$820} \quad \textcolor{red}{\text{Incorrect}}
\]
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