Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = -25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
Describe the basic shape of the graph and where it is located in the Cartesian plane. Describe what the graph represents.
Demonstrate your solution for both the number of clerks that will maximize the profit as well as the total maximum profit possible, making sure to include all mathematical work and an explanation for each step.
Analyze why this information is important for managers to know, and explain what could happen if the ideal conditions were not met.