Question

To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The annual cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be the number of cars and y be the number of students.
a.

Write an expression for total cost.

b.

Write an expression for total revenue.

c.

Write an expression for total profit.

d.

The school offers the course eight times each year. Each time the course is offered, there are two sessions. If they decide to operate five cars, and if four students can be assigned to each car, will they break even?

Answer 1

Answer:

(a) 30,000 + 14,000x (b) 350y (c) 350y - (30,000 + 14,000x) (d) Yes

Step-by-step explanation:

(a) Total cost = 30,000 + 3,000x + 11,000x = 30,000 + 14,000x

(b) Total revenue = 350y

(c) Total profit = Total revenue - total cost = 350y - (30,000 + 14,000x)

(d) To break even, the total profit of the school should be $0 or more. If they decide to use 5 cars with 4 students assigned to each car, 16 times a year (eight times with two sessions each) then we have a total  of 20 students. Using our formula total profit is equal to 350(320) - (30,000 + 14000(5)) = $112,000 - $100,000 = $12,000 profit