SOLUTION: The manager of big box store has found that if the price of a pillow is p(x)= 65 - x/8, then x pillows will be sold. The expression for the total revenue from the sale of x pillows

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The manager of big box store has found that if the price of a pillow is p(x)= 65 - x/8, then x pillows will be sold. The expression for the total revenue from the sale of x pillows      Log On


   

Question 1205964: The manager of big box store has found that if the price of a pillow is p(x)= 65 - x/8, then x pillows will be sold. The expression for the total revenue from the sale of x pillows is R(x) = 65x - x2 (x squared) /8. Find the number of pillows that will produce maximum revenue.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

R%28x%29+=+65x+-+x%5E2%2F8
derivate
R'%28x%29+=+65+-+2x%2F8
R'%28x%29+=+65+-+x%2F4

find the value of x that makes first derivative equal to zero

0=65-x%2F4
x%2F4=65
x=65%2A4
x=260

max{ 65x+-+x%5E2%2F8 } = 8450 at x+=+260
the number of pillows that will produce maximum revenue is 260