Problem $2$ CL: $20/$Others: $25,$ You want to design a cylindrical vessel $($closed at the top and bottom$)$ at a minimal cost. The next is a set of specifications the vessel should have:

$-$Total internal capacity of the vessel $=V_T$

$-$Maximum height to diameter ratio $=R_{\text{m}\text{a}\text{x}}$

Minimum height to diameter ratio $=R_{\text{m}\text{i}\text{n}}$

$-1-$

ES$604$ Engineering Optimization

Assignment #$1$

Due: $14/08/2024$ at $03$:$30$ p$.$m$.$

The price of the metal used for the vessel is $P(US\frac{\text{\$}}{m^2})$

i$)$ Formulate the corresponding optimization problem to calculate the optimal dimensions of the vessel.

ii$)$ Draw a schematic of the objective function and feasible region using the following values $(V_T=10m^3,R_{\text{m}\text{a}\text{x}}=10,R_{\text{m}\text{i}\text{n}}=1$ and $P=$$$\frac{30}{m^2}).$please show the schematic representation of the question