Tuesday

July 29, 2014

July 29, 2014

Posted by **Joshua** on Sunday, May 3, 2009 at 2:13pm.

Suppose a business can sell x gadgets for p=250-0.01x dollars apiece, and it costs the business c(x)= 100+25x dollars to produce x gadgets. Determine the production level and cost per gadget required to maximize profit.

I saw in one problem in the book that they determine the production level by setting the derivative of the cost equal to the derivative of the revenue. (I don't know if this is the way that it always needs to be done-- I don't really understand how to find production level.)

Going on this, I know that

p(x)= r(x) - c(x)

where p=profit, r=revenue, and c= cost

which means that p(x)+ c(x) = r(x)

therefore:

250 -.01x + 100 + 25x= 350+24.99x= r(x)

But if we set c'(x)= r'(x) we get

25=24.99 which doesnt work.

Also, if we set p'(x)=0 (to maximize profit) we end up with -.01=0.... which doesn't work, again.

How should I solve this?

**Related Questions**

Math - A large factory knows that if it sells it's new gadgets for $10 each, it ...

math - The fixed costs of oreparting a business are the costs include rent, ...

Math - The equation y = 240x + 720 gives the cost y (in dollars) when x gadgets ...

calculus - I'm having trouble with these two problems. If someone can help me ...

mat115 - A pack of 250 key blanks costs $23.50. What is the unit price? I know ...

economics - Hey can someone tell me how to graph this in excel please. Thanks. ...

College Economics - Hey can someone tell me how to graph this in excel please. ...

Optimization - What are some ethical issues that could surface in the business ...

Calculus - I am having a lot of trouble doing these types of problems. Can ...

calculus - i am struggling with the concept of optimization. does anyone have ...