Steps to Linear Programming

1. Steps to Linear Programming • 1. Define variables. • 2. Write a system of inequalities. • 3. Graph the system of inequalities. • 4. Find the coordinates of the vertices of the feasible region. • 5. Write an expression to be maximized or minimized. • 6. Substitute the coordinates of the vertices in the expression. • 7. Select the greatest or least result to answer the problem.

2. As a receptionist for a veterinarian, one of Dolores Alvarez’s tasks is to schedule appointments. She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The veterinarian cannot do more than 6 surgeries per day. The office has 7 hours available for appointments. If an office visit costs $55 and most surgeries cost $125, find a combination of office visits and surgeries that will maximize the income the veterinarian practice receives per day.

3. Dean Stadler has 20 days to plant corn and soybeans. The corn can be planted at a rate of 25 acres per day and the soybeans at a rate of 20 acres per day. He has 450 acres available for planting these two crops. Write a system of inequalities to represent the possible ways Mr. Stadler can plant the available acres. • a. Draw the graph showing the feasible region and list the co-ordinates of the vertices of the feasible region. • b. If the profit on corn is $26 per acre and the profit on soybeans is $30 per acre, how much of each should Mr. Stadler plant? What is the maximum profit? How much of each should Mr. Stadler Plant if the profit on corn is $29

4. A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5,000 for every acre he plants with wheat and $3,000 for every acre he plants with barley. His use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires just 1 gallon per acre.