The appliance manufacturer evaluates that profit y (in dollars) made by producing x cooktops per month is given by equation
\(10x + 0.5x^{2} - 0.001x^{3} - 5000\)
where 0 <= x <= 450.
a. How many cooktops should be produced to start generating the profit?
b. For what range of values of x is company's profit greater than $15,000?