The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The shop owner needs to determine the total daily cost of making x cookies. Which of the following linear equations represents the cost, C, in dollars?

Rationale

C = 0.19x + 41.26 represents the total daily cost of making x cookies.

This equation correctly incorporates the variable cost per cookie, $0.19, multiplied by the number of cookies sold (x), plus the fixed expenses of $41.26, resulting in the total cost for the cookie shop.

A (C=4.6x+995) YOUR ANSWER

This equation suggests a cost per cookie of $4.60, which is unreasonably high for a cookie shop and does not match the given cost. Additionally, the fixed cost of $995 is far too high compared to the provided fixed expenses of $41.26, making this option incorrect.

B (C=0.046x+2) YOUR ANSWER

Here, the cost per cookie is inaccurately set at $0.046, which is significantly lower than the actual cost of $0.19. Furthermore, the fixed cost of $2 does not align with the stated fixed expenses of $41.26, leading to an incorrect representation of total costs.

D (C=1.2x+212.26) YOUR ANSWER

This option indicates a cost per cookie of $1.20, which is also too high compared to the correct cost of $0.19. The fixed cost of $212.26 is excessive and does not reflect the accurate total fixed expenses, rendering this equation incorrect.

Conclusion

The total daily cost for the cookie shop is accurately described by the equation C = 0.19x + 41.26, where $0.19 reflects the variable cost per cookie and $41.26 represents the fixed costs. The other options fail to align with the provided cost structure, confirming that choice C is the only suitable representation of the shop's total costs.

C = 0.19x + 41.26 represents the total daily cost of making x cookies.

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