Formulate an NLP
The energy used in compressing a gas in 3 stages from an initial pressure
“I” to a final pressure “F” is given by the formula
K*(sqrt(p1/I) + sqrt(p2/p1) + sqrt(F/p2) – 3)
where K is some arbitrary positive constant. Formulate an NLP
whose solution describes how to minimze the energy used in compressing the gas.
a) Using the values I=1 (atmosphere) and F=10, solve the NLP numerically.
b) Based on the optimal p1 and p2 values you got, write down a formula
for the optimal p1 and p2 as a function of I and F.
c) Prove that your conjecture is indeed optimal (take the gradient, etc.)