Linear Programming

Question

A student earns $12 per hour for tutoring and $6 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 =

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

C. Graph the system of inequalities in part (b). Use only the first quadrant and its boundary, 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.

E. Complete the missing portions of the statement below. Note that the maximum value of the objective function occurs at one or more vertices of the graphed region.

Answer 1

Hi, Titus!

Here is how to start this problem:

A. $12 per hour for x hours is 12x, $6 per hour for y hours is 6y, so z = 12x + 6y

B. We have to have more information on the constraints in order to get an area with four vertices. Do they tell you what the limit is for the tutoring or teacher's aide hours? Is he expected to attend a certain number of classes each day?

C., D. and E. depend on the information you are given for the constraints.

If you can give me more data, I can provide a better answer.

I hope this helps!

Karen