Section 52b x C Chegg Study | Guided So x ? ? www.webassign.netweb/Student/Assig

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Section 52b x C Chegg Study | Guided So x ? ? www.webassign.netweb/Student/Assignment-Responses/last?dep-1843 3507 . 3. +-3 polnts WaneAC 5.2.033. My Notes Ask Your Teacher Because of sales by a competing company, your company's sales of virtual reality video headsets have dropped, and your financial consultant revises the demand equation to 700 where g 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 still amounts to headset. 80 per (a) What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) ?| How many headsets will your company sell at this level of profit? (Give your answer to the nearest whole number.) headsets (b) How much, to the nearest $1, should your company charge per headset for the maximum profit? 4. -2 points WaneAC7 5.2.061 The FeatureRich Software Company sells its graphing program, Dogwood, with a volume discount. If a customer buys x copies, then he or she pays $400Vx. It cost the company $5,000 to develop the program and $2 to manufacture each copy. If a single customer were to buy all the copies of Dogwood, how many copies would the customer have to buy for FeatureRich Software's average profit per copy to be maximized? My Notes Ask Your Teacher copies Type here to search 2:35 PM 4/2/2018

Explanation / Answer

3.

Revenue, R(q)=p*q=700q^{0.65}

Cost, C(q)=80q

So profit is, M(q)=R-C=700q^{0.65}-80q

M'=700*0.65/q^{0.35}-80

M''=-700*0.65*0.35/q^{1.35}<0

Hence any critical point given by M'=0 is point of maxima

M'=0 gives

q=143.52~144

4.

Revenue, R(x)=400 sqrt{x}

Cost, C(x)=5000+2x

Average profit, P(x)=(R(x)-C(x))/x=(400 sqrt{x}-5000-2x)/x=400/sqrt{x}-5000/x-2

P'(x)=-200/x^{1.5}+5000/x^2=0 gives

x=625

So, customer would have to buy 625 copies

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