The monthly profit from the sale of a product is given by p = 36x -0.2x2 - 100 dollars. (a) what level of production maximizes profit? units (b) what is the maximum possible profit?

The level of production that maximizes the profit is 90 units.

The maximum possible profit is 1520 dollars

Step-by-step explanation:

The profit is modeled by a quadratic equation, thus we can find its vertex x coordinate and we will find the number of units that maximizes the profit using the vertex formula

For

Then we can find the profit just replacing the number of units on the profit equation.

a) What level of production maximizes profit?

We can first write the profit equation in descending order.

Thus we get for the coefficients a = -0.2 and b = 36.

Replacing them on the vertex formula

We get

Simplifying we get

The level of production that maximizes the profit is 90 units

b) What is the maximum possible profit?

We can replace the vertex x coordinate on the profit function, which is finding the value of the profit P(x) for x = 90 units.

Simplifying we get

The maximum possible profit is 1520 dollars

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.