Question

A company's monthly profit, P, from a product is given by P = −x2 + 105x − 1050, where x is the price of the product in dollars. What is the lowest price of the product, in dollars, that gives a monthly profit of $1,550?

Answer 1

If the monthly profit is to be 1550, then we know P=1550, therefore:\[1550=-x^2+105x-1050\]then simply re-arrange this to form a standard quadratic equation as follows:\[x^2-105x+2600=0\]solve this to find two possible values for x and select the smallest value for the answer.