Question

2. Zelda runs a factory that prints books. a) Let po be the rate in thousands of pages per hour, that a printing press in Zelda's factory printing pages t hours after 7 AM i. Give a practical interpretation of the integral Pdt. ii. Give a practical interpretation of the expression ple}dt. iii. Zelda doesn't know when the printing press started running, but that it was sometime before 7 AM. She also knows that it printed 300.000 pages between the time it started running and 10 AM. Write an expression involving one or more integrals for the number of pages, in thousands, the printing press produced between the time it started running and 7 AM (b) The graph below shows the marginal revenue MR dashed) and marginal cost MC (solid), in dollars per book, of printing q copies of a certain book. y (dollars per book) - MC V=NR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1. For what value(s) of in the interval 10.201 is the cost function minimized! il. Let (o)be Zelda's profit from printing copies of the book. What are the critical points of #() in the interval (0,207 iii. For what values of g in the interval 0,20) is the profit function () maximized? iv. For what values of q in the interval (0,20) is the profit function () concave down? Express your answer as one or more intervals.

Answer 1

2 ( PCE) at 15 The above integral gives the total no. of pages printed from t = 1.5 to t = 8 hours ic, from 8.30AM to 3 PM 1/3 | Pct) dt 1 of papers printed from t= 4 to t = 7 le) from 11 AM to 2pm printed per hour os areage no. of papers from llam to 2pm 300.000 = (pet) dt = IPCt) dt & Spas dt (C) pages o printed V tom t to 7AM

to TAM .. pages printed - 300,000 - from time t pats at pages printed from 7am to IOAM