Minor Video has opened a new store renting videocassettes.Fixed costs are $60,000,and the variable cost per unit is $1.50.The average sale is $5 per customer.Use the following axes to determine the break-even quantity graphically.Next,refine your solution by solving it algebraically.(Show your work for credit. )
A)The break-even quantity is fewer than or equal to 10,000 rentals.
B)The break-even quantity is more than 10,000 rentals and fewer than or equal to 20,000 rentals.
C)The break-even quantity is more than 20,000 rentals and fewer than or equal to 25,000 rentals.
D)The break-even quantity is more than 25,000 rentals.

Question

Minor Video has opened a new store renting videocassettes.Fixed costs are $60,000,and the variable cost per unit is $1.50.The average sale is $5 per customer.Use the following axes to determine the break-even quantity graphically.Next,refine your solution by solving it algebraically.(Show your work for credit. ) 
A)The break-even quantity is fewer than or equal to 10,000 rentals. 
B)The break-even quantity is more than 10,000 rentals and fewer than or equal to 20,000 rentals. 
C)The break-even quantity is more than 20,000 rentals and fewer than or equal to 25,000 rentals. 
D)The break-even quantity is more than 25,000 rentals.

Quizplus · Accepted Answer

To determine the break-even quantity graphically, we need to plot the total cost function and the total revenue function on the same graph and find the point of intersection.

Total cost function = Fixed cost + Variable cost = $60,000 + $1.50Q where Q is the quantity of rentals

Total revenue function = Average sale per customer x Quantity of rentals = $5Q

Setting total cost equal to total revenue:

$60,000 + $1.50Q = $5Q

$3.50Q = $60,000

Q = 17,142.86

So, the break-even quantity is more than 10,000 rentals and fewer than or equal to 20,000 rentals.

To refine the solution algebraically:

Break-even quantity = Fixed cost / (Price per unit - Variable cost per unit)

Q = $60,000 / ($5 - $1.50)

Q = 17,142.86

Again, we get the same result, so the answer is still B.

Minor Video Has Opened a New Store Renting Videocassettes