Question #3c139

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Answer 1 · 2017-09-11T11:45:46

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

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]