Question

A small cell phone company estimates that by charging I dollars for each phone, they can sell 104 - 0.5x phones per day The quadratic function R(x) = -0.52% + 104x is used to find the revenue. Rreceived when the selling price of a phone is = dollars. Find the selling price that will give the maximum revenue and then find the amount of the maximum revenue Answer. The selling price that will give maximum revenue is Select an answer The maximum revenue is Select an answer Select an answer Note Round any numeri dollars per phone scunal places. If there are multiple answers, separate them with commas phones per dollar phones Points possible: 4 dollars This is attempt 1 of 2 none of these units

Answer 1

$100 per phone, and the maximum revenue is $5,200.

To find the selling price that will give the maximum revenue, you need to determine the price (xx) that maximizes the revenue function R(x)=−0.52x2+104xR(x)=−0.52x2+104x.

The maximum revenue occurs at the vertex of the quadratic function, and the x-coordinate of the vertex can be found using the formula x=−b2ax=−2ab​, where aa is the coefficient of the quadratic term (-0.52) and bb is the coefficient of the linear term (104).

In this case:

a=−0.52a=−0.52

b=104b=104

Now, calculate xx:

x=−1042(−0.52)x=−2(−0.52)104​

x=−104−1.04x=−−1.04104​

x=100x=100

So, the selling price that will give the maximum revenue is $100 per phone.

To find the maximum revenue, substitute this selling price back into the revenue function R(x)R(x):

R(100)=−0.52(100)2+104(100)R(100)=−0.52(100)2+104(100)

R(100)=−0.52(10,000)+10,400R(100)=−0.52(10,000)+10,400

R(100)=−5,200+10,400R(100)=−5,200+10,400

R(100)=5,200R(100)=5,200

The maximum revenue is $5,200.

So, the selling price that will give the maximum revenue is $100 per phone, and the maximum revenue is $5,200.