A company produces two products: A and B. The profit per unit of product A is 4, and the profit per unit of product B is 5. The production process for each product requires two resources: labor and material. For product A, the production process requires 2 hours of labor and 3 units of material. For product B, the production process requires 4 hours of labor and 5 units of material. The company has a total of 200 hours of labor and 300 units of material available. Determine the production levels of products A and B that maximize the company’s total profit.
A company produces two products: A and B. The profit per unit of product A is 4, and the profit per unit of product B is 5. The production process for each product requires two resources: labor and material. For product A, the production process requires 2 hours of labor and 3 units of material. For product B, the production process requires 4 hours of labor and 5 units of material. The company has a total of 200 hours of labor and 300 units of material available. Determine the production levels of products A and B that maximize the company’s total profit.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...
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A company produces two products: A and B. The profit per unit of product A is 4,
and the profit per unit of product B is 5. The production process for each product
requires two resources: labor and material. For product A, the production process
requires 2 hours of labor and 3 units of material. For product B, the production
process requires 4 hours of labor and 5 units of material. The company has a total
of 200 hours of labor and 300 units of material available. Determine the production
levels of products A and B that maximize the company’s total profit.
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Step 1: Introduce to the given information
VIEWStep 2: Define the variables and write the constraints equation
VIEWStep 3: Sketching the graph of the first inequality
VIEWStep 4: Sketching the graph of the second inequality
VIEWStep 5: Sketching the graph of third and fourth inequalities
VIEWStep 6: Determining the intersection points of the lines 1 and 2
VIEWStep 7: Sketching the graph of the system of inequalities.
VIEWStep 8: Sketching the graph of the solution region and determining the corner points
VIEWStep 9: Determining the maximum profit
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