A small business makes cookies and sells them at the farmer's market. The fixed monthly cost for use of a Health Department–approved kitchen and rental space at the farmer's market is $790. The cost of labor, taxes, and ingredients for the cookies amounts to $0.24 per cookie, and the cookies sell for $6.00 per dozen. (See Example 7) Write a linear cost function representing the cost C(x) to produce x dozen cookies per month. Write a linear revenue function representing the revenue R(x) for selling x dozen cookies. Write a linear profit function representing the profit for producing and selling x dozen cookies in a month. Determine the number of cookies (in dozens) that must be produced and sold for a monthly profit. If 150 dozen cookies are sold in a given month, how much money will the business make or lose?

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.

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