To establish a driver education school, organizers must decide how many cars, in
ID: 2903611 • 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, 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?
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
Fixed cost = 30000
For x cars, total annual cost for the cars = 3000x dollars
For x instructors, total annual cost for the instructors = 11000x dollars
For y students, total revenue gained = 350y dollars
a)
Totat cost, C = 30000 + 3000x + 11000x
C = 14000x + 30000 dollars
b) Revenue, R = 350y dollars
c)
Profit = Revenue - Cost
P = 350y - (14000x + 30000)
P = 350y - 14000x - 30000 dollars
d)
8 times a year
Each time, there are 2 sessions
So, a total of 16 sessions conducted.
In each of those 16 sessions, 5 cars are operated.
So, x = 5
Now, this means, a total of 16*5 = 80 courses are delivered.
Since each course can have 4 students, a total of 320 students.
So, y = 320
P = 350y - 14000x - 30000
P = 350(320) - 14000(5) - 30000
P = 12000
So, they get a profit of $12,000
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