-p.-116.jpeg "1. 4-3 Application Problem (lo 7 8) P. 116")
Application Problem: Inventory Management
4-3 Application Problem (LO 7-8) p. 116
Problem Statement
A company produces two products, A and B, which require different amounts of time on the company's two machines, Cutting and Finishing. The time required for each product on each machine is shown in the table below.
| Product | Cutting (minutes) | Finishing (minutes) |
|---|---|---|
| A | 10 | 20 |
| B | 15 | 10 |
The company has 480 minutes of Cutting time and 600 minutes of Finishing time available per day. The profit on each unit of A is $20, and the profit on each unit of B is $30. How many units of each product should the company produce daily to maximize profit?
Solution
Let's break down the problem step by step:
Step 1: Define the Decision Variables
Let x be the number of units of product A to produce, and y be the number of units of product B to produce.
Step 2: Write the Objective Function
The profit function can be written as:
Maximize P = 20x + 30y
Step 3: Write the Constraints
The constraints are based on the availability of Cutting and Finishing time.
For Cutting time: 10x + 15y ≤ 480
For Finishing time: 20x + 10y ≤ 600
Step 4: Solve the Linear Programming Problem
Using a linear programming solver or graphical method, we get:
x = 20 units of product A y = 20 units of product B
Interpretation
The company should produce 20 units of product A and 20 units of product B daily to maximize profit.
