b$)$ A canal section is to be lined to resist erosion using stratification of up to the three layers $($base$,$ middle, and top$)$ layers. Total thickness of the lining should not exceed $20$ mm $.$ The base, middle, and top layer of lining can erode $0\mathrm{.}6,0\mathrm{.}3$ and $0\mathrm{.}1m\frac{m}{?}$ year due to water current. Total life of the lining should be at least $50$ years. The costs of the base, middle and top layers are Rs$.300,400,$ and $500$ per mm thickness, respectively. Formulate a Linear Programming $($LP$)$ problem and solve it using Simplex tables.