MAXIMIZE PROFIT HELP!! PLEASE!

[ariana07]

A company operates 32 corner stores each of which returns an average profit of $1000 per week. A market study reveals that the opening of each new store decreases the average profit by $22. How many new stores should be opened to maximize profit?

PLEASE anything will help!

 

[tkhunny]

What's the current profit?
What is the profit obtained by opening one more store?

 

[mmm4444bot]

PLEASE anything will help!

What will help us is you asking specific questions about the part(s) in this exercise that you do not understand. Otherwise, how are we supposed to figure out what you understand thus far and where you are stuck?

Do you realize that you need to create a function for total profit, whose independent variable represents the number of new stores? If you do, then start by writing down the meaning of this variable.

x = the number of new stores added

Think about the questions asked by tkhunny. Use the symbol x to write symbolic expressions for the increased number of total stores and the reduced new average profit for each. The product of these two expressions is what defines the total-profit function.

Then, it's off to differentiating the function, followed by seeking the value of x that makes f`(x) = 0.

Again, if you ever see anything here (or elsewhere) that you don't fully understand, please feel free to post a specific question about it.

Cheers

 

[ariana07]

Alright what i'm having troubles with is creating this equation to represent what's going on, I know Profit= revenue - cost, I was thinking P(x)= (32 + x)(1000 - 22x) but i don't know if that makes sense

 

[mmm4444bot]

I know Profit= revenue - cost

You are correct! But, in this exercise, they've already done that calculation for you. They give you: Profit = 1000.

(In other words, they bypassed the revenue and cost functions, in this exercise.)

1000 is the profit per store (averaged), when there are 32 stores. This average profit changes, when new stores are added.



P(x)= (32 + x)(1000 - 22x) but i don't know if that makes sense

It's perfect!!

The expression 32 + x represents the number of stores, and the expression 1000 - 22x represents the profit.

Now that you have the total profit function P, can you finish the exercise?