We found that the marketing research department for the company that manufacture

Question

We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions: p(x) = 80 - 3x R(x) = xp(x) = x(80 - 3x) Price-demand function Revenue function where p(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have domain 1 lessthanorequalto x lessthanorequalto 16. Find the output that will produce the maximum revenue.

Explanation / Answer

given revenue R(x)=x(80-3x)

R(x)=(80x-3x2)

for maximum revenue dR/dx =0 ,d2R/dx2 <0

80-6x=0

x=80/6

x=40/3

d2R/dx2 =-6 <0

output that produces the maximum revenue =40/3 million chips

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