Question 1201982
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Answer: <font color=red size=4>P = -x^2 + 36x - 87</font>


Work Shown:


Profit = Revenue - Cost
P = R - C
P = (-0.6x^2 + 8x) - (0.4x^2 - 28x + 87)
P = -0.6x^2 + 8x - 0.4x^2 + 28x - 87
P = (-0.6x^2-0.4x^2) + (8x+28x) - 87
P = -x^2 + 36x - 87


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Edit: The student requested finding the vertex.


There are few ways to find the vertex. One way is to note that the parabola y = -x^2+36x-87 is of the form y = ax^2+bx+c
a = -1
b = 36
c = -87


The vertex is of the form (h,k)
The steps to calculate h would be:
h = -b/(2a)
h = -36/(2*(-1))
h = -36/(-2)
h = 18
This is the x coordinate of the vertex.


Plug that into the function to find its paired y coordinate.
y = -x^2+36x-87
y = -18^2+36(18)-87
y = 237
The vertex is located at (h,k) = <font color=red>(18, 237)</font>


It means that <font color=red>selling 18 thousand pretzels will bring in a max profit of 237 thousand dollars.</font>
The point (18, 237) is the highest point on the parabola.
I recommend using a graphing app such as Desmos or GeoGebra to confirm the answer is correct. 
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