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4.03 Application Problems Using Linear Programming

Complete the following linear programming problems.

1. You have started an exercise program consisting of walking and running each day. You plan to walk 10 to 20 minutes each day and run 30 to 45 minutes each day. You only have time to spend a total of 60 minutes for both running and walking. If you burn 6 calories per minute walking and 15 calories per minute running, how much time should you spend on each activity to maximize the number of Calories burned?

Constraints: Graph:

[pic]

Objective Function: M = 6x+15y

Use the above to complete the following:

You should walk       minutes per day and run       minutes per day to burn a maximum of       calories.

2. John owns a house painting company. An experienced crew can prep 6 rooms and paint 2 rooms in a week. A novice crew can prep 2 rooms and paint 2 rooms in a week. An experienced crew gets paid $1000 per week and a novice crew gets paid $750 per week. To stay on schedule, John needs at least 12 rooms prepped and 8 rooms painted per day. How many weeks should each crew be scheduled to minimize cost?

Constraints:

[pic]

Objective Function: C = 1000x + 750y

Graph the constraints and complete the process to find the minimized cost.

Graph:

Then complete the following:

John should schedule       experienced crews and       novice crews to obtain a minimum cost of      .

3. A farmer plants white rice and brown rice on 10 acres of land. He must use pesticide on all 10 acres and he has 18 liters of pesticide to use. White rice requires 2 liters of pesticide per acre and brown rice requires 1 liter of pesticide per acre. If he can earn $5000 for each acre of white rice and $3000 for each acre of brown rice, how many acres of each should he plant to maximize his earnings? What are his maximum earnings?

Let x represent the white rice.

Let y represent the brown rice.

Constraints:

[pic]

Objective Function: R =      x +      y

Graph:

The farmer should plant       acres of white rice and       acres of brown rice to obtain his maximum earnings of      .

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