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3 – 4 Linear Programming Word Problems

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.

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3 – 4 Linear Programming Word Problems

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  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 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

  4. 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. Graph the system of inequalities. Example 4-3a

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

  7. Substitute the coordinates of the vertices into the function. • 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 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

  9. Example 4-3b

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