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Statistics Help

**Question: **The owner of an ice cream franchise must pay the parent company $2800 per month plus 5% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $4400per month for items such as utilities and labor. The cost of ice cream and supplies is 65% of the revenue.(a) Express the owner's monthly expense E in terms of R. E =

(b) Express the monthly profit P in terms of R. P = (c) Determine the monthly revenue needed to break even.= $ Edit

**Answer: **To answer this question, we need to determine the break even point for a revenue stream R. The break even point is the point at which total cost and revenue are equal. Or

Revenue - Total Cost = 0

Total cost is the sum of both fixed costs and operating costs:

Revenue - fixed costs -operating costs = 0

Fixed costs are costs that do not vary. This problem's fixed costs are:

$2800 per month to the parent company

$4400 per month for utilities and labor

Operating costs vary, commonly as a function of product but in this case just revenue. This problem's operating costs are:

0.05 * R (5% of monthly revenue to parent company)

0.65 * R (65% of monthly revenue for supplies).

So our equation is:

R - 2800 - 4400 - 0.05R - 0.65R = 0

0.30R -7200 = 0

0.3R = 7200

R = 7200/0.3 = $24,000

Edit

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