Question 5070
Look at the first few situations...

1.6*2000 --> 3200
1.7*1900 --> 3230
1.8*1800 --> 3240
1.9*1700 --> 3230


This gives you the answer of 1.80 as the amount to charge to maximum their revenue. How do to this algebraically?


Well, looking at the above sequence, we have in general:
(1.6+0.1x)*(2000-100x), where x is just a number, 0, 1, 2, 3, 4 etc


so revenue, r = (1.6+0.1x)(2000-100x). This expands to be
r = {{{3600-160x+200x-10x^2}}}
r = {{{-10x^2 + 40x + 3600}}}
r = {{{-x^2 + 4x + 360}}}


Differentiate, giving dr/dx = -2x + 4.


So when is this equal to zero? ie when does the curve "turn"?
-2x+4 = 0
--> 2x = 4
so x = 2 but is it a max or min?


{{{d^2r/dx^2 = -2}}}: negative --> therefore max.


So, the maximum occurs when x = 2, ie should charge 1.60+2(0.1) = 1.80, which agrees with our common sense approach we did first.


jon.