Question

Dan and Juanita are arguing, again! Dan says the revenue function for the

campus bookstore R(v) = p(x) times x, will have a maximum value of less $35 million dollars if:
P(x)=-3/2x+112 in millions of dollars and the units sold is x is the number of units
sold. Juanita has not done the problem, but she is sure the bookstore has a larger maximum
profit. Show who is right.

Please help me!

Answer 1

Find

R(V)

• p(x)×x
• x(-3/2x+112)
• -3/2x²+112x

Now

• y=-3/2x²+112x

Find vertex x coordinate

• -b/2a
• -112/-2(-3/2)
• -37.3

Put in equation

• y=-3/2(-37.3)²+112(-37.3)
• y=-2086.9-84+4177.6
• y=$6264.6
• y=$62.64M

As a is negative parabola is facing downwards hence vertex is minimum .

So minimum value is $62M which is far more than given .