Question 163627: the revenue, R, of an electronics manufacturer for selling x handheld organizers is given by R=0.25x^2-100x. The revenue of a competing manufacturers for selling similar products is R=75x. Under what circumstances will both manufacturers have the same revenue?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! he revenue, R, of an electronics manufacturer for selling x handheld organizers is given by R=0.25x^2-100x. The revenue of a competing manufacturers for selling similar products is R=75x. Under what circumstances will both manufacturers have the same revenue?
:
Just make the two expression equal to each other and find x
0.25x^2-100x = 75x
:
.25x^2 - 100x - 75x = 0
:
.25x^2 - 175x = 0
;
Get rid of the decimal, multiply equation by 4
x^2 - 700x = 0
:
Factor out x
x(x - 700) = 0
:
Two solutions:
x = 0 (when they both sell nothing, of course they will be equal)
and
x = 700 units sold they will be equal, probably the solution they want
:
:
Check for equal revenue
75(700) = $52,500
:
.25(700^2) - 100(700) =
122500 - 70000 = $52,500
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