An appliance manufacturer estimates that the profit y (in dollars) generated by producing x cooktops per month is given by the equation y = 10x + 0.5x2 − 0.001x3 − 6000, where 0 ≤ x ≤ 450.

Question

Graph the equation.

(b) How many cooktops must be produced to begin generating a profit? (Round your answer to the nearest whole number.)

 cooktops

(c) For what range of values of x is the company's profit greater than $15,000? (Enter your answer using interval notation. Round numerical values to the nearest whole number.)

 

Answer 1

Here are some hints to answer these three questions.

1. In a polynomial, the constant term (the one without a variable) is the y-intercept. Only one of the graphs shown has a y-intercept equal to the constant term of the polynomial. Can you find it?
2. Below the x-axis, the profit is negative (you're losing money). Above the x-axis, profit is positive. Where does the graph cross the x-axis?
3. Draw a horizontal line through y = 15,000 all the way out to x = 450. The portion of the graph above this line is the interval where the profit exceeds $15,000.