Answer to Question #222596 in Operations Research for HANNA

Question

Problem 5: To establish a driver educational 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 30000 birr. The annual cost per car is 3000 birr.

The cost per instructor is 11000 birr and one instructor in needed for each car.

Tuition for each student is 350 birr. 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 the decided to operate five cars, and if

four students can be assigned to each car, will they break-even?

Answer 1

a)Total cost= Fixed cost + (cost per car +cost per instructor) 

Total cost= 30,000+(3000x+11000x)=30,000+14000x

b) Total Revenue =number of students * amount paid by each student

Total Revenue= 350y 

c) Total profit = Total revenue -total cost =350y-(30,000+14000x)

d) Yes it will break even .

To break even, the total profit should be $0 or more . In a scenario where the school utilizes 5 cars with 4 students assigned to each car, 16 times a year (eight times with two sessions each) then the total number students will be 20. Therefore, profit is equal to 350(320) - (30,000 + 14000(5)) = $112,000 - $100,000 = $12000 profit