Adding tax to items

[kickingtoad]

Homework 12-6, problem 5

A company manufactures and sells x TVs per month. The monthly cost and price-demand equations are:

\(\displaystyle C(x)=72000+60x\)
\(\displaystyle p(x)=200-\frac{x}{30}\)

I already found these solutions:
Max revenue is at 3000 TVs
Max profit is at 2100 TVs
Max profit is $7500
The price that should be charged to maximize profit is $130

(E) If the government decides to tax the company $ 5 for each set it produces, how many sets should the company manufacture each month to maximize its profit?

I'm not sure how to go about this question. I thought I'd add $5 to $60 so it's 65x, but that didn't work.

 

[lookagain]

[/b]

I'm not sure how to go about this question. I thought I'd add $5 to $60 so it's 65x, but that didn't work.

Let x = the number of television sets

In your direction of solving, why don't you still use \(\displaystyle C(x) = 72000 - 60x - 5x = 72000 - 65x?\)

\(\displaystyle R(x) = x \big(200 - \frac{x}{30} \big) = 200x - \frac{x^2}{30}\)

\(\displaystyle P(x) = \bigg(200x - \frac{x^2}{30}\bigg) - (72000 - 65x)\)


\(\displaystyle A) \ \ Simplify \ \ P(x).\)

\(\displaystyle B) \ \ Find \ \ P'(x).\)

\(\displaystyle C) \ \ Set \ P'(x) \\ = \ 0 \ and \ solve \ for \ positive \ values \ of \ x.\)