Question

A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 100 x plus 4000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make?

Answer 1

The equation described above can also be written as,
                    y = -x² + 100x + 4000
To get the number of notebooks that will give them the maximum profit, we derive the equation and equate to zero.
                  dy/dx = -2x + 100 = 0
The value of x from the equation is 50. Then, we substitute 50 to the original equation to get the profit. 
                   y = -(50^2) + 100(50) + 4000 = 6500
Thus, the maximum profit that the company makes is $6,500/day.