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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.2: Systems Of Linear Equations In Two Variables
Problem 41E
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Question
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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