A manufacturer sells watches for $75 per unit. The fixed costs related to this product are $10,000 per month, and the variable costs are $55 per unit. This gives a profit function , where r is the revenue per unit and c is the variable cost per unit. If the manufacturer has a profit of zero, how many watches were sold?
A) 1,000
B) 5,000
C) 500
D) 133
E) 182

Question

A manufacturer sells watches for $75 per unit. The fixed costs related to this product are $10,000 per month, and the variable costs are $55 per unit. This gives a profit function  , where r is the revenue per unit and c is the variable cost per unit. If the manufacturer has a profit of zero, how many watches were sold? ​
A) 1,000 
B) 5,000 
C) 500 
D) 133 
E) 182

Quizplus · Accepted Answer

At zero profit, the revenue and cost are equal:

r x = c x + 10000

Substituting the given values:

75x = 55x + 10000

20x = 10000

x = 500

Therefore, 500 watches were sold to break even and obtain zero profit.

A Manufacturer Sells Watches for $75 Per Unit