P = 100x^(-1) + x ( pi + 8 - 2sqrt(3)/ 4 take the derivative, set to 0
P' = -100x^(-2) + ( pi + 8 - 2sqrt (3) ) / 4 = 0 multiply through by x^2
[ ( pi + 8 - 2sqrt (3) / 4 ] x^2 - 100 = 0
[ pi + 8 - 2sqrt (3) ] x^2 = 400
x^2 = 400 / [ pi + 8 - 2sqrt (3) ] take the positive root
x = 7.218
Sub this back into P to find the minimum P ≈ 27. 7 m
We can verify that this is the minimum ........
P " = 200/ x^3
Subbing in x = 7.218 will produce a positive....thus...x = 7.218 produces a minimum value
