| Author |
Comment/Response |
Hila
|
 01/04/13 2:44pm
I defined a function ProfitRetailSolo, and one of the parameters it takes is R.
I can not get closed form expressions for the value of R that maximizes ProfitRetailSolo. SO I am doing some numerical analysis.
As can be seen below I used Reduce and required the first deriviative to equal 0 and the second derivative to be negative.
With the specific values I am using for the other parameters- The output is that there are two values of R for which above holds: R == 73.1497 || R == 77.5785 (see below)
But when I then try to plug back above values in the derivative-- I dont get 0.
Also plotting the ProfitRetailSolo function, it does not have a maximum around R=73.
Can someone help me get correct result for the value of R that maximizes ProfitRetailSolo?
Thanks!
Hila
R1t = N[FullSimplify[
Reduce[{D[ProfitRetailSolo[80, 100, 0.8, 1.5, 0, R, 8], R] == 0,
D[ProfitRetailSolo[80, 100, 0.8, 1.5, 0, R, 8], {R, 2}] < 0,
R < 0.8 100, R > 0.8 80}, R]]]
Out[124]= R == 73.1497 || R == 77.5785
In[122]:= D[ProfitRetailSolo[80, 100, 0.8, 1.5, 0, R, 8], R]
Out[122]= -((
9.31323*10^-10 (-64. +
R)^7 (3.\[VeryThinSpace]+ (-1 +
2.32831*10^-10 (-64. + R)^8) (80.\[VeryThinSpace]+ R)))/(-1 +
2.32831*10^-10 (-64. + R)^8)^2) + (-1 +
2.32831*10^-10 (-64. + R)^8 +
1.86265*10^-9 (-64. + R)^7 (80.\[VeryThinSpace]+ R))/(
2 (-1 + 2.32831*10^-10 (-64. + R)^8))
In[123]:= N[% /. R -> 77.57851923357128`, 20]
Out[123]= 0.0549258
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