# Question 3c139

Sep 11, 2017

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) $\cdot$quantity(Q) , for every increase of $0.25 in price $I = \left(2.25 + 0.25 x\right) \cdot \left(1400 - 100 x\right)$ or

$I = - 25 {x}^{2} + 125 x + 3150$ or

$I = - 25 \left({x}^{2} - 5 x\right) + 3150$ or

$I = - 25 \left\{{x}^{2} - 5 x + {\left(\frac{5}{2}\right)}^{2}\right\} + \frac{625}{4} + 3150$ or

$I = - 25 {\left(x - \frac{5}{2}\right)}^{2} + 3306.25$ , 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 $1400 - 2.5 \cdot 100 = 1175$and maximum income will be $3306.25 # [Ans]