# Sports Shoes

Submitted By sdhussa
Words 1215
Pages 5
High Step Shoes-Student Activity 1
High Step Sport Shoes: A Linear Programming Problem
Linear programming is a method often used to solve large, complicated problems. These problems often require a manager to determine how to use the company’s limited resources most efficiently. In order to see how linear programming is used to solve such problems, let’s investigate a problem experienced at the High Step Shoe factory. The High Step Shoe problem is just a fraction of the size of those actually encountered in the real world.
Step 1: Understanding the problem
Mr. B. Ball, director of manufacturing for the High Step Sports Shoe Corporation wants to maximize the company’s profits. The company makes two brands of sport shoe, Airheads and Groundeds. The company earns \$10 profit on each pair of Airheads and
\$8.50 profit on each pair of Groundeds. The steps in manufacturing the shoes include cutting the materials on a machine and having workers assemble the pieces into shoes.
A = number of pairs of Airheads produced each week
G = number of pairs of Groundeds produced each week
Mr. B. Ball’s goal is to make the most money or maximize his profits. Using A and G, write a function to model the profit.
1. Profit = _______ A + _______ G
This function is called the objective function.
The number of machines, workers, and factory operating hours put constraints on the number of pairs of shoes that the company can make. High Step Sport Shoe Corporation has the following constraints. There are 6 machines that cut the materials,
850 workers that assemble the shoes, and the assembly plant works a 40 hour week.
Step 2: A System of Inequalities: Constraints
Machine Cutting Constraint Inequality
Each hour, each cutting machine can do 50 minutes of work. How many minutes of work can 6 machines do in a 40 hour work week?
2. _____ machines x ______ min/hr x...

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