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4) A sausage company makes two brands of sausages: Link and Patty. Link brand uses 1 pound of pork and 3 pounds of beef while the Patty brand uses 2 pounds of pork and 3 pounds of beef. A case of Link sausage requires 3 hours of labor while a case of Patty sausages requires 1 hour of labor. The company has at most 1000 pounds of pork and 1800 pounds of beef available to make sausages. The total work hours are restricted to no more than 1200 hours. The profit on a pound of Link sausage is $3 while the profit on a pound of Patty sausage is $2. How many pounds are required to maximize profit? a) Write the objective function. Define the variables. b) Write the system of inequalities describing the constraints. c) Graph the system. Shade and Label the feasibility region. Label corner points after completing part d.

4) A sausage company makes two brands of sausages: Link and Patty. Link brand uses 1 pound of pork and 3 pounds of beef while the Patty brand uses 2 pounds of pork and 3 pounds of beef. A case of Link sausage requires 3 hours of labor while a case of Patty sausages requires 1 hour of labor. The company has at most 1000 pounds of pork and 1800 pounds of beef available to make sausages. The total work hours are restricted to no more than 1200 hours. The profit on a pound of Link sausage is $3 while the profit on a pound of Patty sausage is $2. How many pounds are required to maximize profit? a) Write the objective function. Define the variables. b) Write the system of inequalities describing the constraints. c) Graph the system. Shade and Label the feasibility region. Label corner points after completing part d.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Section d)** **Find all corner points. List these below and on the graph. Show all computations.** (Here, you would conduct a detailed computation to find all the corner points of the feasible region in a graph. This might involve solving a system of equations derived from constraints in a linear programming problem, then plotting these points on a graph.) --- **Section e)** **How many pounds of each should be produced to maximize profit? Use a table.** (You should use a table format to demonstrate the quantities of each product that would result in maximum profit. This involves evaluating the profit at each corner point found in section d and indicating the optimal production quantities.) --- **Section f)** **What is the maximum profit?** (______) (Here, you would calculate the maximum profit by substituting the optimal production quantities into the profit equation.) **Note**: Since the diagram or graph is not visible, this explanation serves as an instructional guide on how to approach the problem.
Transcribed Image Text:**Section d)** **Find all corner points. List these below and on the graph. Show all computations.** (Here, you would conduct a detailed computation to find all the corner points of the feasible region in a graph. This might involve solving a system of equations derived from constraints in a linear programming problem, then plotting these points on a graph.) --- **Section e)** **How many pounds of each should be produced to maximize profit? Use a table.** (You should use a table format to demonstrate the quantities of each product that would result in maximum profit. This involves evaluating the profit at each corner point found in section d and indicating the optimal production quantities.) --- **Section f)** **What is the maximum profit?** (______) (Here, you would calculate the maximum profit by substituting the optimal production quantities into the profit equation.) **Note**: Since the diagram or graph is not visible, this explanation serves as an instructional guide on how to approach the problem.
**Problem 4 Description:** A sausage company produces two brands of sausages: Link and Patty. The Link brand uses 1 pound of pork and 3 pounds of beef, while the Patty brand uses 2 pounds of pork and 3 pounds of beef. Each case of Link sausage requires 3 hours of labor, whereas each case of Patty sausages requires 1 hour of labor. The company has a maximum of 1000 pounds of pork and 1800 pounds of beef available for sausage production. The total work hours are limited to at most 1200 hours. The profit per pound of Link sausage is $3, and the profit per pound of Patty sausage is $2. The problem is to determine how many pounds of each sausage are required to maximize profit. **Tasks:** a) **Objective Function and Variable Definition:** - Write the objective function. - Define the variables. b) **System of Inequalities:** - Write the system of inequalities describing the constraints. c) **Graphing the System:** - **Graph the system.** - **Shade and label the feasibility region.** - **Label corner points** after finishing part d. **Graph Explanation:** The graph is a standard coordinate plane grid meant for plotting. It allows you to visually represent the inequalities and identify the feasible region where the constraints overlap, aiding in finding the optimal solution for maximizing profit. Note: There is no specific graph already plotted; users need to plot based on the constraints given.
Transcribed Image Text:**Problem 4 Description:** A sausage company produces two brands of sausages: Link and Patty. The Link brand uses 1 pound of pork and 3 pounds of beef, while the Patty brand uses 2 pounds of pork and 3 pounds of beef. Each case of Link sausage requires 3 hours of labor, whereas each case of Patty sausages requires 1 hour of labor. The company has a maximum of 1000 pounds of pork and 1800 pounds of beef available for sausage production. The total work hours are limited to at most 1200 hours. The profit per pound of Link sausage is $3, and the profit per pound of Patty sausage is $2. The problem is to determine how many pounds of each sausage are required to maximize profit. **Tasks:** a) **Objective Function and Variable Definition:** - Write the objective function. - Define the variables. b) **System of Inequalities:** - Write the system of inequalities describing the constraints. c) **Graphing the System:** - **Graph the system.** - **Shade and label the feasibility region.** - **Label corner points** after finishing part d. **Graph Explanation:** The graph is a standard coordinate plane grid meant for plotting. It allows you to visually represent the inequalities and identify the feasible region where the constraints overlap, aiding in finding the optimal solution for maximizing profit. Note: There is no specific graph already plotted; users need to plot based on the constraints given.
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