Acompany plans to sell embroidered hats for $15 each. the company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). what is the minimum number of hats the company must sell to make a profit?
a.151
b.401
c.529
d.601

The selling price is $15
The variable cost is given by a quadratic equation with a y-intercept of 7920 and a vertex of (150,9000). The equation of that quadratic equation is:
y = Ax2 + Bx + C or (x - h)^2 = 4a (y - k)
(0-150)^2 = 4a (7920 - 9000)
4a = -125/6
y = (-6/125) (x - 150)^2  + 9000

The profit is
P = 15x - [(-6/125) (x - 150)^2  + 9000]x

We can differentiate the equation or substitute the choices and see which would give a profit. So, the answer is:
D. 601

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