Thread: Max and Min values question.

A local furniture manufacturer sells cedar pato sets. The company can sell x units each month at a price of p(x)=1000-x in dollars, where the cost, C, of producing x units per day is, C(x)=3000+19x^2.

Determine a) the price that will maximize the profits
and b) the break even point.

Not sure where to start...

Originally Posted by Harne

A local furniture manufacturer sells cedar pato sets. The company can sell x units each month at a price of p(x)=1000-x in dollars, where the cost, C, of producing x units per day is, C(x)=3000+19x^2.

Determine a) the price that will maximize the profits
and b) the break even point.

Not sure where to start...

Lets see, we sell at BUT the cost to produce it is

So wouldn't the profit be

So find the derivative of x in the profit formula and set x into the price formula.

Originally Posted by janvdl

Lets see, we sell at BUT the cost to produce it is

So wouldn't the profit be

So find the derivative of x in the profit formula and set x into the price formula.

No the sales are units per day when the price per unit is , so
the revenue is , and the cost to produce units is .

So the profit is:

.

RonL

Originally Posted by CaptainBlack

No the sales are units per day when the price per unit is , so
the revenue is , and the cost to produce units is .

So the profit is:

.

RonL

Ah ok, didnt realise that i should have multiplied with an extra