# Max and Min values question.

• May 23rd 2007, 08:00 AM
Harne
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... :(
• May 23rd 2007, 10:21 AM
janvdl
Quote:

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 \$\displaystyle 1000 - x \$ BUT the cost to produce it is \$\displaystyle 3000 + 19x^2 \$

So wouldn't the profit be \$\displaystyle 1000 - x - (3000 + 19x^2) \$ :)

So find the derivative of x in the profit formula and set x into the price formula. :)
• May 23rd 2007, 12:56 PM
CaptainBlack
Quote:

Originally Posted by janvdl
Lets see, we sell at \$\displaystyle 1000 - x \$ BUT the cost to produce it is \$\displaystyle 3000 + 19x^2 \$

So wouldn't the profit be \$\displaystyle 1000 - x - (3000 + 19x^2) \$ :)

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

No the sales are \$\displaystyle 1000-x\$ units per day when the price per unit is \$\displaystyle x\$, so
the revenue is \$\displaystyle (1000-x)x\$, and the cost to produce \$\displaystyle x\$ units is \$\displaystyle 3000+19x^2\$.

So the profit is:

\$\displaystyle 1000x - x^2 -3000 - 19x^2 = -20x^2+1000x -3000\$.

RonL
• May 23rd 2007, 01:00 PM
janvdl
Quote:

Originally Posted by CaptainBlack
No the sales are \$\displaystyle 1000-x\$ units per day when the price per unit is \$\displaystyle x\$, so
the revenue is \$\displaystyle (1000-x)x\$, and the cost to produce \$\displaystyle x\$ units is \$\displaystyle 3000+19x^2\$.

So the profit is:

\$\displaystyle 1000x - x^2 -3000 - 19x^2 = -20x^2+1000x -3000\$.

RonL

Ah ok, didnt realise that i should have multiplied with an extra \$\displaystyle x \$ :)