How many fans should be produced for max profit?

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It costs the Fresh Air Fan Company (20x+100) dollars to produce x ceiling fans. They sell the fans for (300-2x) dollars each. How many fans should the company produce each month to maximize their profit?

So for the vetex, I got (50,100000)
I don't know how to figure it out after that. I'm thinking the number of fans they should produce each month is 50?
 
Re: How many for max profit

AirForceOne said:
It costs the Fresh Air Fan Company (20x+100) dollars to produce x ceiling fans. They sell the fans for (300-2x) dollars each. How many fans should the company produce each month to maximize their profit?

So for the vetex, I got (50,100000)
Click to expand...
Vertex of your profit (sales - cost) function? Show us what you think the profit function is, and then how you came up with that for the vertex (of the parabolic profit function).

AirForceOne said:
I don't know how to figure it out after that. I'm thinking the number of fans they should produce each month is 50?
Click to expand...
If the profit function is an upside down parabola, then its maximum value occurs at the vertex. First get the vertex right.
 
Well, I did

y = (1000+20x)(300-2x)
y = 300000 - 2000x + 6000x - 40x^2
y = -40x^2 + 4000x + 300000
y = -40(x^2 - 100x + 2500) + 100000
y = -40(x - 50)^2 + 100000
vertex: (50, 100000)

and the parabola is right side up...
 
AirForceOne said:
It costs the Fresh Air Fan Company (20x+100) dollars to produce x ceiling fans. They sell the fans for (300-2x) dollars each. How many fans should the company produce each month to maximize their profit?

So for the vetex, I got (50,100000)
I don't know how to figure it out after that. I'm thinking the number of fans they should produce each month is 50?
Click to expand...

Profit = receipts - cost

If the price per fan when you sell x fans is (300 - 2x), then the amount received for selling x fans is x(300 - 2x)

The cost for producing x fans is (20x + 100).

Therefore,
Profit = x(300 - 2x) - (20x + 100)

Try working with THAT equation.
 
Wow that's complicated. Never thought of that. Will try it out.

Thanks a ton!
 
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