Need help with this calculus/business math question...fast!!
The monthly demand, x, of a compact disc is related to the price, p dollars per disc by the following equation:
p(x)=-0.0004x + 6
The total monthly cost for pressing and packaging x copies is given by
C(x)=600 + 2x - 0.0002x^2
A) What is the production level that minimizes the total cost?
B) What is the revenue function?
C) What is the profit function?
D) What is the production level that maximizes the profit?
Please try and show work if possible. I really need some help with this one. Thanks!
Re: Need help with this calculus/business math question...fast!!
The maximum and minimum of a function occurs when the derivative of a function is equal to 0. To find the value of x that minimises a function find the derivative and put it equal to 0 and solve the equation you get for x.
The monthly revenue is the demand multiplied by the price. That's x*p(x)
The profit is revenue - cost. That's x*p(x) - C(x)
Now you have the function for profit