Question

Question #3c139

Answer 1

To maximize the income rental price should be `$2.875`.

Explanation:

Rental price is `P=$2.25` , Quanity on rental is `1400`

Let `x` be he number of `$0.25` increase in price .

Income(I) = Price(P) `*` quantity(Q) , for every increase of

`$0.25` in price `I = (2.25+0.25x) * ( 1400 -100x)` or

`I = -25x^2 +125x +3150` or

`I = -25(x^2 -5x) +3150` or

`I = -25{x^2 -5x +(5/2)^2} +625/4 +3150` or

`I = -25(x-5/2)^2 + 3306.25` , So `I` is maximum when

`x=2.5` .To maximize the income rental price should be

`P=2.25+2.5*0.25=$2.875` for Quanity on rental iof

`1400-2.5*100 =1175` and maximum income will be

`$3306.25` [Ans]