Question 180862
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:
With a 12 gallon tank, a Jupiter gets 22 mi/gal. Engineers estimate that every 2
 gallon increase in tank size causes gas mileage to decrease by 1 mi/gal. 
What should the size of the tank be for the Jupiter to have the greatest range
 (number of miles on a tank of gas)?
:
Let x = increase in size (in gal) of the tank
then
y = range of the tank (in miles)
:
It says, "every 2 gallon increase in tank size causes gas mileage to decrease by 1 mi/gal."
From this we can say it decreases .5 mi mpg, for each 1 gal increase (.5x)
:
Range = mpg * gal
y = (22-.5x)(12+x) 
FOIL
y = 264 + 22x - 6x - .5x^2
:
y = -.5x^2 + 16x + 264; a quadratic equation
:
Max range occurs at the axis of symmetry, can be found using x = {{{(-b)/(2a)}}}
In this equation: a = -.5, b = 16
x = {{{(-16)/(2*-.5)}}}
x = {{{(-16)/(-1)}}}
x = +16 gal increase for max range
:
Therefore: 12 + 16 = 28 gal tank will give max range
:
Actual range: (22 - .5(16)) * 28 = 392 mi