26. 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?
Answer: C
C = 0.19x + 41.26
The equation that represents the total daily cost of making x cookies is C = 0.19x + 41.26. This equation incorporates both the variable cost per cookie and the fixed expenses associated with running the shop.
A) C = 4.6x + 995
This option suggests a cost structure that implies a significantly higher variable cost per cookie, which is not supported by the information given. The fixed cost of $995 is also unrealistic for a small cookie shop, making this option incorrect.
B) C = 0.046x + 2
While this option reflects a variable cost, the per cookie cost of $0.046 is inaccurately low compared to the provided cost of $0.19. Additionally, the fixed cost of $2 is far too low to reflect the shop's actual expenses of $41.26, rendering this option incorrect.
C) C = 0.19x + 41.26
This option accurately represents the total cost, where $0.19 is the cost per cookie, and $41.26 reflects the fixed expenses. This aligns perfectly with the shop owner's current expense structure, making it the correct choice.
D) C = 1.2x + 212.26
This option presents a much higher variable cost per cookie and an inflated fixed cost, which does not match the shop's actual expenses. Such high values are not consistent with the small cookie shop's financials, making this option incorrect.
Conclusion
C = 0.19x + 41.26 is the only equation that accurately combines both the variable cost per cookie and the fixed expenses of the cookie shop. The other options either miscalculate the variable cost or present unrealistic fixed costs, thereby failing to reflect the shop's actual financial situation.