Question

For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000 . The maximum capacity of the company is 120 items.
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!



Answers to some of the questions are given below so that you can check your work.



Assuming that the company sells all that it produces, what is the profit function?
P(x)=

Answer 1

Assuming that this company sells all that it produces, the profit function would be given by P(x) = -0.5(x - 100)² + 5,000 - 50x - 100.

What is profit?

In Economics, profit can be defined as a measure of the amount of money (revenue) that is generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

This ultimately implies that, all producers generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.

Mathematically, the profit function P(x) of a business firm simply refers to the revenue function R(x) minus the cost function C(x):

P(x) = R(x) - C(x)

Where:

• R(x) represents how much it takes in.

• C(x) represents how much it spends.

Substituting the given parameters into the formula, we have;

P(x) = -0.5(x - 100)² + 5,000 - (50x + 100)

P(x) = -0.5(x - 100)² + 5,000 - 50x - 100

Read more on maximized profit here: brainly.com/question/13800671

#SPJ1