SOLUTION: 1. A company that produces cells for solar collectors finds through experience that on the average it can sell x cells per day at a selling price (in dollars) of p(x) = 100 � 0.05x

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Question 129106: 1. A company that produces cells for solar collectors finds through experience that on the average it can sell x cells per day at a selling price (in dollars) of p(x) = 100 � 0.05x (p is called the demand function). The cost function C(x) for producing x cells per day is C(x)= 4000 + 60x � 0.01x^2

A. Write the revenue function R(x).

B. Write the profit function P(x).

C. Find the value of x that maximizes profit, and find the maximum profit.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
a)

The revenue can be found by this general formula:

Revenue=Number of units sold*price of each unit

So in our case,

Start with the given equation

Plug in

Distribute

Rearrange the terms

So the revenue function is

b)

The profit can be found by:

Profit=Revenue-Cost

So

Plug in and

Distribute the negative

Combine like terms

To find the max profit, we need to graph the profit function

And by using the calculators vertex function, we find that the vertex occurs at

Now plug in into

Simplify

So the maximum profit is $6,000