The owner of an ice cream franchise must pay the parent company $1,200 per month plus 7% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,300 per month for items such as utilities and labor. The cost of ice cream and supplies is 53% of the revenue. Determine the monthly revenue needed to break even.
A)$5,833
B)$8,750
C)$3,500
D)$1,400
E)$1,100

Question

Quizplus · Accepted Answer

To break even, the total costs must equal the total revenue. The total costs include the fixed payment to the parent company, the percentage of revenue paid to the parent company, the fixed operating cost, and the cost of ice cream and supplies. Let's denote the monthly revenue as $R$.The total cost $C$ can be calculated as follows:$$C = \$1,200 + 0.07R + \$2,300 + 0.53R$$Combining like terms gives:$$C = \$3,500 + 0.6R$$For the franchise to break even, $C = R$, so:$$\$3,500 + 0.6R = R$$Solving for $R$, we subtract $0.6R$ from both sides to get:$$0.4R = \$3,500$$Dividing both sides by $0.4$ gives:$$R = \frac{\$3,500}{0.4} = \$8,750$$Therefore, the monthly revenue needed to break even is $8,750.

The Owner of an Ice Cream Franchise Must Pay the Parent