Question

The demand equation for your company's virtual reality video headsets is 2,000 where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $130 per headset (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(4)- R(q) (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) 95 headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function P"(4) Evaluate P(q) at your critical point. The result is Select-, which means that the profit is Select at the critical point, and the critical point is a maximum

Answer 1

2 .ftn! Manufacturing and shipping c酞 ¢130 pes headset nd cut the ekly Cst evenue ona Revenue, RC)- P. 2 R(2) 00.? -0.3 :. Here ase have to fnd out that -130 -0.3 -> 140030 づ 130 63

0.3 &#58-1093-2 2=&758 headley i.-Hexe oe have 92位atest t 3,000 (2758 · -130(8758 5 l &泉07、4-35854D 153667-9 . Ci) Secemd cieri vaive test: uoe kno that, - 13 D - 130 "Then PnC2) 스 1400 (-0.3 . 2 -0.3-1 Hence , theォesult negative . cohrch means that the p9ld maximum at -the caitrcal peint.