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Linear Programming Example 2 :
This example will show you how linear programming can help you determine which job to take. Linear Programming Example 2

Slide 2:
While at college, you pick up two part-time jobs to help pay for your expenses. You earn $10 per hour for tutoring and $7 per hour as a teacher’s aide. In order to have enough time for studies, you can work no more than 20 hours each week. The tutoring center requires that each tutor spend between 3 hours and 8 hours each week tutoring. Determine the number of hours the student should work at each job so that you can maximize your paycheck. What is the maximum amount of money you can earn each week?

Slide 3:
First define your variables: (what are the quantities being described)? X = tutoring hours Y = teacher’s aide hours The identify your objective function: (what are you trying to maximize or minimize)? Z=10x + 7y Remember: you will not use this equation until the end

Slide 4:
Now write the constraints: You can’t work more than 20 hours a week so… You can only work between 3 and 8 hours at the tutoring center so… AND you can’t work a negative amount of hours so… Now to the graph:

Slide 5:
This time the only equation we need to manipulate is the first: X-int: X + 0 = 20 X = 20 Y – int: 0 + y = 20 Y = 20 The equation below represents two vertical lines.

Slide 6:
The shading is under the purple line and between the red lines. The region is then a quadrilateral.

Slide 7:
This vertex is (3,17) This vertex is (8,12) (3,0) (8,0) Test the vertices in the objective function:

Slide 8:
Objective Function: z = 10x + 7y (3,0): z = 10(3) + 7(0) = 30 (8,0): z = 10(8) + 7(0) = 80 (3,17): z = 10(3) + 7(17) = 149 (8,12): z = 10(8) + 7(12) = 164 We were trying to maximize what we earned so the max is (8,12): 8 hours tutoring, 12 hours as a teacher’s aide to make $164!