Question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

StartLayout Enlarged Left-Brace 1st Row y = 35 x 2nd Row y = negative 0.05 (x minus 400) squared + 9,942 EndLayout
the number of sweatshirts that generate the maximum income
the number of sweatshirts that generate the minimum cost
the number of sweatshirts for which the difference between cost and income is greatest.
the number of sweatshirts for which cost and income are equal

Answer 1

The solution(s) are the x-value(s) where 35x (revenue) equals −0.05(x−400)^2 + 9,942 (cost). So it gives the number(s) of sweatshirts for which income and cost are equal (the break-even production level(s)).