To establish a driver education school, organizers must decide how many cars ins
ID: 444439 • Letter: T
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 $2700. The cost per instructor is $10,000 and one instructor is needed for each car. Tuition for each student is $375. 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?
Explanation / Answer
a. Total cost = annual fixed cost+annual cost for cars+annual cost for instructors
let number of cars be "x".
annual cost of cars = 2700x. annual cost of instructors = 10,000x.
Thus, total cost = 30,000+2700x+10,000x = 30,000+12,700x
b. total revenue = number of students*tuition for each student = 375y.
c. total profit = revenue - costs = 375y - 30,000 - 12,700x
d. Number of sessions = 8*2 = 16 session per year
Total cost = 30,000+12,700x. if "x' = 5, then cost = 30,000+12,700*5 = $93,500
Number of students = 4 per car. total students per session = 4*5 cars = 20 students. fees per student = 375. Total revenue per session = 20*375 = $7,500
Total revenue = revenue per session*number of sessions = 7500*16 = 120,000
as total revenues (120,000) is greater than total costs (93,500), the school will cross the break even point and will earn revenues.
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