A utilities company would like to transfer energy to its customers such that its daily cost of transmission is mini$-$ mized. It has nuclear reactors in each of the following cities: Sacramento, Houston and Atlanta. The daily energy capacities of these reactors are $4150$ KwH$,3650$ KwH$,$ and $5000$ KWH respectively. The company's clients are in L$.$A$.,$ Birmingham and Denver and have daily demands of $2500$ KwH$,4500$ KwH and $5500$ KwH respectively. These demands must be satisfied. The following table gives the dollar cost of unit energy transfers from source to destination cities. $ spent per KwH transferred Sacramento Houston Atlanta L$.$A$.$ Birmingham Denver $466595552532684458212=213=221=$ Use the following non$-$negative decision variables: $111=$ Number of KwH transferred from Sacramento to L$.$A$.$ Number of KwH transferred from Sacramento to Birmingham Number of KwH transferred from Sacramento to Denver Number of KwH transferred from Houston to L$.$A$.$ Number of KwH transferred from Houston to Birmingham Number of KwH transferred from Houston to Denver $131=$ Number of KwH transferred from Atlanta to L$.$A$.232=$ Number of KwH transferred from Atlanta to Birmingham $133=$ Number of KwH transferred from Atlanta to Denver A$)$ State the objective function of the problem $222=223($a$)$ min $46$x$11+55\mathrm{.}212+68213+65621+25$x$22+44\mathrm{.}623+95231+32$x$32+58133($b$)$ max $46211+65\mathrm{.}212+95$x$13+55\mathrm{.}221+25222+32\mathrm{.}623+68231+44\mathrm{.}632+58133($c$)$ max $46211+55\mathrm{.}212+68213+65\mathrm{.}221+25\mathrm{.}222+44\mathrm{.}623+95\mathrm{.}231+32+32+58833($d$)$ min $46$x$11+65\mathrm{.}212+95\mathrm{.}213+55221+25\mathrm{.}22+32\mathrm{.}623+68231+44\mathrm{.}632+58133$B$)$ State the supply $($capacity$)$ constraints of the problem. $($a$)211+212+213<5000$; $221+222+2233650$; $131+232+133<4150($b$)211+212+213<4150$; $221+222+223<3650$; $131+232+233<5000($c$)2$u$1+221+231<4150$; $212+222+232<3650$; $213+123+133<5000($d$)211+221+131<4150$; $212+222+132<5000$; $213+223+133<3650$ C$)$ State the demand constraints of the problem. $($a$)211+212+213=2500$; $221+222+223=4500$; $231+232+133=5500($b$)211+221+131=5500$; $212+222+232=4500$; $213+223+233=2500($c$)211+221+231=2500$; $212+222+232=4500$; $213+223+233=5500($d$)211+212+213=2500$; $221+222+2235500$; $231+232+233=4500$D$)$ Suppose you set up the following Excel spreadsheet to solve the problem: A B I $$ D E Optimal Decision Variable Values Sacramento Houston Atlanta $23$ O L$.$A$.$ Birmingham Denver O $456$ o O $0$ Objective Function Coefficients Houston $78$ Atlanta $68$ LA $55$ Sacramento $466595910$ Birmingham Denver $25324458$ II Minimized Objective Function $121314$ Amount Used $0$ IS $16$ RHS Limits $415036500$ Constraints i$($Supply for Sacramento$)$ ii $($Supply for Houston$)$ ili $($Supply for Atlanta$)$ iv $($Demand for L$.$A$.)$ v $($Demand for Birmingham$)$ vi $($Demand for Denver$)00181920$ SOOO $25004500550000$ Use Excel Solver to determine the optimal energy transferring scheme. What is its optimal cost? $($a$)$ $o $($b$)$ $$540,400$ II $($c$)$ $$565,450($d$)$ $$751,500($e$)$ $$791,900$E$)$ Which source city has its energy capacity underutilized by $300$ KwH in the optimal solution? $($a$)$ Sacramento $($b$)$ Houston $($c$)$ Atlanta $($d$)$ None of the above