Maximize Profit (Calc I): C(x)=x^3-60x^2+1400x+1000 for 0<=x<=50

[Vladd29]

i have a question here that says
"The total cost of producing x units of a product is given by C(x)=x^3-60x^2+1400x+1000 for 0<=x<=50

The Product sells for $563 per unit, what production level maximizes profit?

Im not even sure you can get max profit from just a cost function. If i was also given a demand function, i know how to do this, but just a cost function? No idea whatsoever. Do i take deriv then plug in 50? then plug in 0 take the difference and thats my x? I have no idea where to begin.

 

[Deleted member 4993]

i have a question here that says
"The total cost of producing x units of a product is given by C(x)=x^3-60x^2+1400x+1000 for 0<=x<=50

The Product sells for $563 per unit, what production level maximizes profit?

Im not even sure you can get max profit from just a cost function. If i was also given a demand function, i know how to do this, but just a cost function? No idea whatsoever. Do i take deriv then plug in 50? then plug in 0 take the difference and thats my x? I have no idea where to begin.

For 'x' units sold:

Profit = 563*x - (x^3-60x^2+1400x+1000)

Now maximize it!

 

[Vladd29]

For 'x' units sold:

Profit = 563*x - (x^3-60x^2+1400x+1000)

Now maximize it!

you're a life saver! i had no idea you can get a function from 563. that amazed me, i got the answer! thanks for helping