Linear Programming: A company manufactures two products A and B, and each of these products must be processed on two different machines. Product A requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product B requires 3 minute of work time per unit on machine 1 and 2 minutes of work time on machine 2. Each day 100 minutes are available on machine 1 and 200 minutes are available on machine 2. The profit of each unit of product A is $50 and the profit of each unit of product B is $60. (Let x = number of units of product A and y = number of units of product B). Identify the variables. Set up the objective function. Give the constraints in mathematical expression. Graph the constraints and identify the solution. How many units of each product should be produced daily in order to maximize the company’s profit? What is that maximum profit daily?
Linear Programming: A company manufactures two products A and B, and each of these products must be processed on two different machines. Product A requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product B requires 3 minute of work time per unit on machine 1 and 2 minutes of work time on machine 2. Each day 100 minutes are available on machine 1 and 200 minutes are available on machine 2. The profit of each unit of product A is $50 and the profit of each unit of product B is $60. (Let x = number of units of product A and y = number of units of product B). Identify the variables. Set up the objective function. Give the constraints in mathematical expression. Graph the constraints and identify the solution. How many units of each product should be produced daily in order to maximize the company’s profit? What is that maximum profit daily?
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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Linear Programming:
A company manufactures two products A and B, and each of these products must be processed on two different machines. Product A requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product B requires 3 minute of work time per unit on machine 1 and 2 minutes of work time on machine 2. Each day 100 minutes are available on machine 1 and 200 minutes are available on machine 2. The profit of each unit of product A is $50 and the profit of each unit of product B is $60.
(Let x = number of units of product A and y = number of units of product B).
- Identify the variables.
- Set up the objective function.
- Give the constraints in mathematical expression.
- Graph the constraints and identify the solution.
- How many units of each product should be produced daily in order to maximize the company’s profit?
- What is that maximum profit daily?
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