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

Answer:

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

Step-by-step 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.

Answer 2

Answer:

Break even quantity and sales

Step-by-step explanation:

Given are a system of equations one representing the sales revenue and next the cost for production.

we know that in any business sales revenue-cost = profit.

Normally business people keep a margin over cost and sell.

But here when the two equations are solved simultaneously we have sales revenue = cost

i.e. the Break even point where there is no profit or no loss.

So the solution to the system of equations as

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

gives the break even point

The solution (x,y) represents x =break even quantity produced and y = break even sales