A laptop company is choosing which components they want to put into th

Given: A laptop company is choosing which components they want to put into their next model. This model laptop will sell for $2000, and every additional component will bring the selling price up an additional $200. However, the company predicts that each time they increase the price, the number of sales will drop by around 5% from the base prediction.

Asked: What is the best number of components to upgrade in order to maximize revenue?

Let the number of components be x and base volume prediction be V.

R = Revenue = Price * Volume = ($2000 + $200x) (V - 5% xV) = $200V (10 + x)(1 - 5x/100) = $200V (10+x)(1-x/20) = $10V (10+x)(20-x) = $10V (200 +10x - xˆ2) = $10V (225 - 25 + 10x - xˆ2) = $10V (225 - (x-5)ˆ2)

To maximize revenues x = 5
Maximum Revenue = $10V *225 = $2250V

IMO B