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.

y=35x; y=-0.05(x-400)^2+9,492

What does the solution of the system represent in this context?

Answer 1

Break even point or shut down point or no profit point.

Explanation:

The given system of equations is

`y=35x`

`y=-0.05(x-400)^2+9492`

The first equation in the system of equations, y represents the money collected from selling sweatshirts. It means first equation represents the revenue function.

In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. It means second function represents the cost function.

The solution of given system of equation it the intersection point of both functions. It means

`Revenue = Cost`

So, get

`Profit = Revenue - Cost = 0`

It total cost is equal to total revenue, then it is called no profit or break even point.

Therefore, the solution of the system represent the quantity of sweatshirts where cost and revenue are equal, and profit is 0.