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?

P = −25x2 + 300x;

To look for the maximum P Is needed to take the derivative of P dP/dx which is = -50x + 300. Making dp/dx =0 we have: 0=-50x + 300 so x will be 6 and the maximum daily profit will be 900 units