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Demand,Revenue, & the Largest Reduction to maximize Revenue

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200 DVD players are sold per week for $300 each. For each $10 rebate (reduction in sale price), 20 additional DVD players are sold.

Find the demand, the revenue, and the largest reduction (multiple of 10) to maximize revenue.

Cost: c(x)
Marginal Cost: c'(x)
Revenue: R(x)= x(p(x))
Demand: p(x)
Marginal Revenue: R'(x)
Profit: P(x)=R(x) - c(x)

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Let x = number of $10 reductions in price

R(x) = p * R(x) = (300 - 10x)(200 + 20x) = 60000 + 4000x - 200x^2

For ...

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