Answer:
We should not go up.
Step-by-step explanation:
Currently, the product sells for $10 and 1000 people buy it each month. So, we currently make a profit of .
We have the option to raise the price in increments of a dollar. Let the extra dollar(s) be x and let P(x) be our profit.
For <em>each </em>dollar we raise, we will <em>lose</em> 100 customers.
The product is currently $10 and we currently have 1000 customers. So, after x increments, our profit will be:
This is a quadratic. So, to find the maximum profit, we need to find our vertex point.
First, let's convert this to standard form. For the second term, we can factor out a -100. So:
Expand:
Simplify:
Distribute:
So, let's find our vertex. The vertex of a quadratic in standard form is:
The standard form of a quadratic is:
So, from our equation, our a is -100, b is 0, and c is 10000.
Substitute 0 for b and -100 for a:
Evaluate:
Now, we can substitute this back into our equation to find the maximum profit we can make:
Evaluate:
Therefore, to make the maximum profit of $10,000, our x should be 0.
Since x is our price increments, this means that we should <em>not</em> make any changes to the price at all.