Answer:
The constant is 140 and it represent the minimum amount of money they'll make from selling hotdogs when the price is not raised.
Step-by-step explanation:
You're given the equation
y = -8x² + 54x + 140
The result from calculating the equation will give you how much money they made at the end of the day. And x is the amount of $1 price increase they had on the hotdog.
So we assume that they didn't raise the hotdog price at all (so x=0), then we would get:
y = -8(0)² + 54(0) + 140
y = 0 + 0 + 140
y = 140
Read further if you want more explanation...
So if they didn't increase their price at all, they would make at least $140.
Now lets plug in x=1 for a $1 increase in price.
we get
y = -8(1)² + 54(1) + 140
y = 186
ok, we see that the amount of money they made increased to $186 when they raise the price.
Now lets check when we raise the price by $2 (x=2)
y = -8(2)² + 54(2) + 140
y = 216
ok, now the revenue increased to $216
Just one last check, lets see what happen when we raise the price by $3 (x=3)
y = -8(3)² + 54(3) + 140
y = 230
Price increased again to $230.
As you can see, the 140 represent the revenue they make when the price is not raised at all (x=0).
