The owner of an ice cream franchise must pay the parent company $1,100 per month plus 5% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 50% of the revenue. Determine the monthly revenue needed to break even.
A)$3,600
B)$1,620
C)$1,400
D)$8,000
E)$6,545

Question

Quizplus · Accepted Answer

To break even, the total cost must equal the total revenue. The total cost includes the fixed franchise fee, the fixed operating cost, and the variable cost of ice cream and supplies. The total cost equation is: $1,100 + 0.05R + $2,500 + 0.5R. The revenue is simply R. Setting the total cost equal to the revenue gives us the equation: $1,100 + $2,500 + 0.05R + 0.5R = R. Simplifying, we get $3,600 + 0.55R = R, which leads to 0.45R = $3,600. Solving for R gives R = $8,000.

The Owner of an Ice Cream Franchise Must Pay the Parent