3

1
3 4Linear Programming Word Problems
2
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.
• 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.

3
Ex 5
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 crews 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.

1. Define the variables.

Example 4-3a
4

1. Write a system of inequalities.

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
5

1. Graph the system of inequalities.

Example 4-3a
6

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

From the graph, the vertices are at

1. 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
7

1. Substitute the coordinates of the vertices
   into the function.

(m, p) f(m, p)

1. Select the greatest amount and answer the
   question.

Example 4-3a
8
Ex 6
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 crews 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
9
Example 4-3b