You make $20/hour tutoring Chemistry and $16/hour tutoring math

Question

Part 1 of 5:

You make $20/hour tutoring Chemistry and $16/hour tutoring math. Let x represent the number of hours per week you spend tutoring Chemistry and y represent the number of hour per week you spend tutoring math.

Write the objective function, z.

Part 2 of 5:

Using the following information, write the constraints. There should be 4 total including x greater or equal than 0.

You can tutor no more than 18 hours per week
The tutoring center requires that you tutor math at least 6 hours per week.
Part 3
Graph the 4 constraints on the same coordinate plane either by hand or using a graphing utility. Be sure that you shade appropriately and ONLY the region that fits all of the constraints. Submit the graph.ce the demand for math tutors is greater than the demand for chemistry tutors, you must spend at least twice the number of hours tutoring math as you do tutoring Chemistry.

Part 4 of 5:

Give the corner points of your feasible region.

Part 5 of 5:

Use the corner points of your graph to determine the maximum amount of money you can make tutoring each week and how many hours you will spend tutoring each. Show your work using the equation editor! Write your final answer in sentence form.

Answer 1

z=20x +16y = total income from tutoring in chemistry and math

x+y < 18

y> 2x

18 > y > 6, 0< x < 9

(0,18), (3,6) are (0,6) are 3 corner points.

but the income maximizing allocation of time is the 4th corner

(6,12) where y=2x intersects x+y=18

those two lines

z = 20(6) + 16(12) = 120 + 192 = 312

the only other possible answer would

be the corner point (0,18) but z=16(18)- 288<312