To establish a driver education school, organizers must decide how many cars, in
ID: 3141497 • 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 $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, these 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 = $30000( fixed cost ) + $3000 ( cost per car) * x ( number of cars) + $11000( cost per instructor)*x ( number of cars=number of instructors)
B) Total revenue = $350 ( tution fee received from each student ) * y ( number of students)
C) Total profit = total revenue- total cost
Total profit =$350*y-( $30000+$3000*x+$11000*x)
D)the school offers course eight times each year. There are tow sessions for each time. So there are in total 8*2= 16 sessions per year. Each session has 5 cars and 4 students per car. It means there are 4*5= 20 students per session. So there are 16( sessions per year) *20= 320 students per year . So y= 320
There are 5 cars operated. So there are only 5 instructors per car. So x= 5
Total profit = $350*320 ( students per year) - ($ 30000+$3000*5( cars per year) +$ 11000* 5( instructors per year) = $112000-$100000= $12000
They will not break even as they generated profit of $12000.
Had the profit been zero , they would break even.
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