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# Why It Matters

## Solve linear programming problems and understand their applications to manufacturing

### Introduction

A farmer has 100 acres of available land where he wants to plant a mixture of corn, wheat and spinach. It costs him $400 to produce an acre of corn,$160 to produce an acre of wheat, and $280 to produce an acre of spinach. He has a maximum of$20,000 to spend. He makes a profit of $120 per acre on corn,$40 per acre on wheat and \$60 per acre on spinach. How many acres of each crop should he plant? Most of us won’t go into farming after we finish our degree, but we will face similar problems as this farmer. We have limited resources and options on how to invest those resources. How can we maximize our profits based on these options?

### Learning Outcomes

• Graph a system of linear inequalities in 2 variables, shade the appropriate region, find corner points, and optimize an objective function subject to constraints graphically
• Use simplex method to solve a linear programming problem
• Use the dual method to solve a minimization problem