Question

1. An appliance store has been selling 240 microwave ovens at $100 each every month. A market survey indicates that for each $6 increase in the price, the number of microwave ovens sold will decrease by 30 per month. It costs the store $46 to purchase each microwave oven from the manufacturer.

A) Find the demand function, expressing p, the price charged for each microwave oven, as a function of x, the number of microwave ovens sold each month.

B) find the revenue function R(x)

C) Find the price the store should charge for each microwave oven to maximize revenue

D) find the price the store should charge for each microwave oven to maximize profit

Answer 1

A) Consider the poin C240, 100) and (210, 106) Then the demand Runction fs 1O6-100 p-100 C240) 2 10-240 a-240) -30 -100 P -100 (o4r-1) P Ia +148 The cest fcun ction C Ca 4 B) The revenue functon s R (a)aP 2-148) + 14 88 Ra) -2 R'ca) 148 0 C) Set >2 740 > &370 The price P 370 +148 74 The revenue is maeirmum at 14.

The profit s Pa) Ra)- CCx) 148a- 46 +L02 Set Pca 0 -25 l02 0 a255 Thus, P-- 255 148 $ 97 5 The profit is mareimum at 97.