Question

a company plans to sell embroidered hats for $15. 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?

Answer 1

revenue for x hats is y=15x
cost is y=0.4(x-150)^2+9000

So, you want x when

15x >= 0.4(x-150)^2+9000
x >= 262.5

so, at least 263 hats