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kkurt
2 months ago
8

A small business makes cookies and sells them at the farmer's market. The fixed monthly cost for use of a Health Department–appr

oved 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?
Mathematics
1 answer:
Inessa [12.5K]2 months ago
6 0
Cost function: Revenue function: Profit function: Dozens required for a specific profit P. If 150 dozen cookies are sold, the profit is negative, resulting in a loss of $322. Step-by-step explanation: We can enumerate the costs as follows: - Fixed monthly cost of $790. - Variable costs of $0.24 per cookie, equating to (12*0.24) = $2.88 per dozen. We can then construct the cost function C(x) considering C(x) represents the monthly cost and x denotes the number of dozens produced each month. Revenue can be calculated as the price ($6 per dozen) multiplied by the quantity sold, x. The profit is calculated by subtracting the total cost C(x) from the revenue R(x). The required number of dozens for a monthly profit can be derived from the preceding equation for P(x). To achieve a monthly profit P, a certain number of dozens must be sold. When selling 150 dozen cookies, the profit recorded is negative, indicating a loss of $322.
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About 400,000 people visited an art museum in December. What could be the exact number of people who visited the art museum
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2 months ago
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Answer:

160/1001, 175/1001

Step-by-step explanation:

i) We calculate:

₈C₁ methods to select 1 new camera from a selection of 8

₆C₃ methods to select 3 refurbished cameras from a selection of 8

₁₄C₄ methods to select 4 cameras from the total of 14 cameras

The probability formula is:

P = ₈C₁ ₆C₃ / ₁₄C₄

P = 8×20 / 1001

P = 160 / 1001

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ii) For at most one new camera, it means we want either one new camera or none at all. We've calculated the probability of selecting one new camera already. The probability of not selecting any new camera is equivalent to selecting 4 refurbished cameras:

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4 0
3 months ago
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Ben could have sold a maximum of 6 turkey sandwiches.

Step-by-step explanation:

Turkey sandwiches are priced at $2.50, while veggie wraps cost $3.50 at the snack stand.

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2.50x < 16

x

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Ultimately, Ben could sell a maximum of 6 turkey sandwiches.

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2 months ago
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