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IE 7541 Louisiana State University Linear Programming Question

IE 7541 Louisiana State University Linear Programming Question

Question Description

A student earns $15 per hour for tutoring and $5 per hour as a teacher’s aide. Let x=the number of hours each week spent tutoring and y=the number of hours each week spent as a teacher’s aide. Complete parts (a) through (e).

a. Write the objective function that describes total weekly earnings.

z=

(Do not include the $ symbol in your answer.)

b. The student is bound by three constraints. Write an inequality for each constraint.

1. To have enough time for studies, the student can work no more than 22 hours per week.

2. The tutoring center requires that each tutor spend at least four hours per week tutoring.

3. The tutoring center requires that each tutor spend no more than seven hours per week tutoring.


c. Graph the system of inequalities in part (b). Use only the first quadrant and itsboundary, because x and y are nonnegative.

d. Evaluate the objective function for total weekly earnings at each of the four vertices of the graphed region. [The vertices should occur at

(4,0),

(7,0),

(4,18),

(7,15)

(Simplify your answers. Use a comma to separate answers as needed.)

e. Complete the missing portions of the statement below.

The students can earn the maximum amount per week by tutoring for

hours per week and working as a teacher’s aide for

hours per week. The maximum amount that the student can earn each week is

$


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