Question

A lamp has a cost function of C(x) = 2500 + 10x, where x is the number of units produced per day and C(x) is in dollars. The revenue function for these lamps is R (X)= 18x−.001x^2. At least 100 lamps and no more than 2000 lamps may be produced per day.
a. How many lamps should be produced in order to maximize profit (prove this)?
b. What is the cost, in dollars, of producing the number of lamps that maximizes the profit?
c. What is the revenue, in dollars, of producing the number of lamp that maximizes the profit?

Answer 1

P = R - C
P = -2500 + 8 x -.001 x^2
dP/dx = 8 - .002 x
for dP/dx = 0
x = 8/.002 = 4000
so make all you can, 2000

so do C and R with x = 2000