- #1

- 69

- 0

Problem: It costs [tex]C(x)=50+\frac{1}{4}x-\frac{1}{30}x^{2}[/tex] dollars to make x dozen donuts in one day [tex]({0}\leq{x}\leq{40})[/tex] and the donuts sell for 75 cents a dozen. a) What are the Revenue R(x) (gross income) and profit P(x) on x dozen donuts? b) What are the average and marginal profits on 30 dozen donuts?

answers a) [tex]R(x)=.75x dollars ; P(x)=\frac{1}{2}x + \frac{1}{30}x^{2}-50dollars[/tex] b)[tex]Averageprofit=-\frac{1}{6}dollar/dozen; Marginal profit=\frac{5}{2}dollars/dozen.[/tex]

My question deals with the marginal profit in part b. It seems that 75 cents per dozen would have to be an upper limit on profit and the $2.50 would not be possible. If one assumes that there are no costs to producing donuts and all the revenue is going into profit, one could not make more than 75 cents/dozen.

Is it that the cost function is completely unrealistic and just created so one can learn the mechanics of taking derivatives?

Thanks for any comments.