a.The sales level needed to maximize the annual profit is the x-value of the vertex of the quadratic function. The highest point is the vertex of the parabola represented by the equation in the form y=ax2+bx+c with a<0 where the x-coordinate is given by x=−b2a.
Substitute a=−0.0001 and b=70:
So, 350,000 units will maximize the profit.
b.Using the x-value from part (a) and the profit function, the maximum annual profit is:
So, the maximum profit is $12,262,500.