Question

A retailer who sells fashion boots estimates that by selling them for x dollars each, he will be able to sell 70−x boots each week. Use the quadratic function R(x)=−x2+70x to find the revenue received when the average selling price of a pair of fashion boots is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

Answer 1

Answer: $35 is the selling price and $1225 is the maximum revenue.

Step-by-step explanation:

Since we have given that

$R(x)=-x^2+70x$

We need to find the maximum revenue.

So, We will first derivative it w.r.t. x.

So, it becomes,

$R'(x)=-2x+70$

Now, we will find critical points.

So, R'(x) = 0

So, it becomes,

$-2x+70=0\\\\-2x=-70\\\\x=\dfrac{70}{2}=35$

Now, to check whether it yields maximum revenue or not.

So, second derivative w.r.t. x, we get that

R''(x) = -2<0

So, At $35, it yields maximum revenue.

Amount of maximum revenue would be

$R(35)=-(35)^2+70\times 35=-1225+2450=\ 1225$

Hence, $35 is the selling price and $1225 is the maximum revenue.