Question

A company's profit can be modeled by the equation p(u)=−u ^2 +180u+1000 where 'u' is the number of units sold. Find the maximum profit of the company. How many units should the company sell to maximize profit?

Answer 1

The company should sell 90 units to maximize profit.

Step-by-step explanation:

To find the maximum profit of the company, we need to identify the value of 'u' that will maximize the profit function p(u) = -u^2 + 180u + 1000. To do this, we can use the vertex formula for a quadratic equation: u = -b/2a. In this case, a = -1, b = 180, and c = 1000. Substituting these values into the formula, we get u = -180/(2*(-1)) = 90. Therefore, the company should sell 90 units to maximize profit.