*Originally posted by: ***unsped**
the problem is this thread is worded very poorly. this isnt a calculus question so much as its an economic class question. the reason people are finding it difficult is because there are other equations that you are not including, equations you would know if you went to class

im assuming you use both equations to find a condition that is known before hand as its a basic profit maximization question... depending on the type of firm, the profit max condition changes.

for instance a business in a free market situation generally has profit max at

marginal revenue = marginal cost

with the price equation you can easily figure out the revenue equation

marginal revenue is the derivative of revenue, marginal cost is the derivative of cost.

a producer will produce up to a point where the amount of revenue they get for an additional item is equal to thier costs incurred with selling that one item.

since revenue and cost are dependant on quanities, there are derivatives involved.

http://www.digitaleconomist.com/profit.html
MR=P=MC

MC = dC = 30

80-.5x=30

x=100(units)

P=80-.5(100)=30

unless im mistaken, the profit max number of units is 100, plug that back into the price equation and the answer is

**C** 30