1 / 9

# - PowerPoint PPT Presentation

3 – 4 Linear Programming Word Problems. Linear Programming Steps. Define the variables. Write a system of inequalities. Graph the system of inequalities. Find the coordinates of the vertices of the feasible region.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '' - cedric-greene

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 3 – 4Linear Programming Word Problems

• Define the variables.

• Write a system of inequalities.

• Graph the system of inequalities.

• Find the coordinates of the vertices of the feasible region.

Sometimes you may have to solve a system of equations to identify the exact point at which two lines intersect.

• Write the function to be maximized.

• Substitute the coordinates of the vertices into the function.

• Select the greatest or least amount. Answer the problem.

A landscaping company has crews who mow lawns and prune shrubbery. The company schedules 1 hour for mowing jobs and 3 hours for pruning jobs. Each crew is scheduled for no more than 2 pruning jobs per day. Each crew’s schedule is set up for a maximum of 9 hours per day. On the average, the charge for mowing a lawn is \$40 and the charge for pruning shrubbery is \$120. Find a combination of mowing lawns and pruning shrubs that will maximize the income the company receives per day from one of its crews.

• Define the variables.

Example 4-3a

Since the number of jobs cannot be negative, m and p must be nonnegative numbers.

Mowing jobs take 1 hour. Pruning jobs take 3 hours. There are 9 hours to do the jobs.

There are no more than 2 pruning jobs a day.

Example 4-3a

From the graph, the vertices are at

• Write the function to be maximized.

The function that describes the income is

We want to find the maximum value for this function.

Example 4-3a

• Select the greatest amount and answer the question.

Example 4-3a

A landscaping company has crews who rake leaves and mulch. The company schedules 2 hours for mulching jobs and 4 hours for raking jobs. Each crew is scheduled for no more than 2 raking jobs per day. Each crew’s schedule is set up for a maximum of 8 hours per day. On the average, the charge for raking a lawn is \$50 and the charge for mulching is \$30. Find a combination of raking leaves and mulching that will maximize the income the company receives per day from one of its crews.

Example 4-3b