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 and total revenue functions on the same graph and identify the point where they intersect.

Total Revenue = Average Sale * Quantity
Total Cost = Fixed Cost + (Variable Cost per unit * Quantity)

Substituting the given values, we get:
Total Revenue = 5Q
Total Cost = 60,000 + 1.5Q

Setting TR = TC, we get:
5Q = 60,000 + 1.5Q
3.5Q = 60,000
Q = 17,143 (rounded to nearest whole number)

Therefore, the break-even quantity is 17,143 rentals.

Refining the solution algebraically:
To confirm this result algebraically, we can solve for Q by setting TR = TC as follows:

5Q = 60,000 + 1.5Q
3.5Q = 60,000
Q = 17,143

So, the store needs to rent out at least 17,143 videocassettes to break even.

Since the answer choices are given in ranges, we can see that the break-even quantity is between 10,000 and 20,000 rentals, and therefore the best choice is B.

Minor Video Has Opened a New Store Renting Videocassettes