Question

Suppose a business can sell x gadgets for p=250-0.01 dollars a piece, and it costs the business c(x)=1000 + 25 dollars to produce the x gadgets. Determine the production level and the sale price per gadget required to maximize the profit.

Answer 1

Your functions are missing a variable. Double check.

Answer 2

Guessing it means "\(p(x)=250-0.01x\) dollars a piece, and it costs the business \(c(x)=1000 + 25x\) dollars to produce the x gadgets. "

Profict = p(x) - c(x).

Answer 3

Unless one or more of the functions are quadratic or some other model . . .

Answer 4

This is a trivial example if linear; any x>30 will break even and profit increase is only limited by other restrictions on x.

Answer 5

@jessicajuanng , can you verify the form of your equations please?

Answer 6

thanks @CliffSedge I figured out with the help of my friend that x(price)-cost was the equation then I took the derivative!:)