Calculus question, please help?

Question

An electronic manufacturing company has determined that the cost of producing x units of its newest stereo is C(x) = 3500 + 10x ,

and the monthly demand equation for this cost function is p = [40 - (1/1500) x] where x is the number of units and p is the price in

dollars. Use the demand equation to find the revenue equation. Then find the profit equation and use it to compute the profit and

marginal profit for a production level of 2250 units. The marginal profit when 2250 units are produced is _____________dollars?

Answer 1

Cost function C(x) = 3500 + 10x

Demand ( Price ) function p(x) = 40 - (1/1500)x

Revenue equation r(x) = Price function * Number of units

Profit equation= Profit function= s(x) = Revenue function - Cost Function

s(x) = r(x) - c(x)

Profit

Substitute x = 2250

Profit at x=2250

Marginal profit is the derivative (slope )of the profit function.

so take the derivative of p(x) and evaluate it at x = 2250

Apply derivative

Substitute x = 2250

Revenue equation

Profit at 2250 units is 

The marginal profit when 2250 units are produced is 48490 dollars