Q #4. Acme can produce DVD players at a cost of $140 each and market analysis estimates that if the players are sold at x dollars apiece, consumers in a region will buy approximately 2000e^-0.008x machines per week. At what price should the players be sold to maximize profit?
Q #6. If 3xy - 4x^2 = 2y^2 - 5x, then y' =
p(x) = profit = x *(2000e^-0.008x) - 140*(2000e^-0.008x)
dp(x)/dx = 2000e^-0.008x - x *(16e^-0.008x) + 2240e^-0.008x
This provides an example of a maximization problem, differentiation, and equation of a tangent line.