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Answer:
Cost function:
Revenue function
Profit function
Dozens needed for a specific profit P
If 150 dozen cookies are sold the profit is negative, so the business is loosing $322.
Step-by-step explanation:
We can list the costs as:
- Fixed monthly cost, $790/month.
- Variable costs, $0.24/cookie, which are (12*0.24) = $2.88 a dozen.
Then, we can write the cost function C(x) as:
being C(x): the monthly cost and x: the number of dozens produced per month.
The revenue can be calculated as the price ($6 a dozen) multiplied by the number of dozens x:
The profit can be calculated substracting the total cost C(x) from the revenue R(x).
The number of cookies (in dozens) that must be produced and sold for a monthly profit can be calculated from the previous equation for P(x).
For a monthly profit P, the number of dozens that need to be sold are:
If 150 dozen cookies are sold, the profit made is:
The profit is negative, so the business is loosing $322.