Question #3c139

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Answer 1 · 2017-09-11T11:45:46

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

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

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

Income(I) = Price(P) $\cdot$ $*$ quantity(Q) , for every increase of

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

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

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

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

$I = - 25 {(x - \frac{5}{2})}^{2} + 3306.25$ $I = -25(x-5/2)^2 + 3306.25$ , So $I$ $I$ is maximum when

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

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

$1400 - 2.5 \cdot 100 = 1175$ $1400-2.5*100 =1175$ and maximum income will be

$$ 3306.25$ $$3306.25$ [Ans]