Problem $2$: $(30)$

The water engineer of a city's municipal department plans to build a water tank to address the increasing

water demand of the city's fast$-$growing population. The available space for the tank $($excluding access$),$ is

$600f{t}^2.$ The planned inside depth of the tank is $10ft.,$ and it is desired that its length is at least twice its

width $($Length and width are outside dimensions$).$ Space limitations dictate that the width cannot exceed

$20ft.$ The tank will be built with reinforced concrete of $1ft.$ thickness $($walls$,$ base, and cover$).$ The city

seeks to reduce the total cost of the concrete construction. The unit cost of concrete construction, which

includes not only concrete material costs but also formwork and other related costs, is

$\{$:$35\mathrm{.}315f{t}^3)$

Find:

$($a$)$ Formulate the problem indicating decision variables, objective function, and constraints. $(15)$

$($b$)$ Solve the problem using Excel Solver and provide optimal tank dimension and cost. Round off tank

dimensions to the nearest $3".($Hint: Use GRG Nonlinear solving method and initial non$-$zero

decision variable values$)(15)$