Three plants$-$P$1,$ P$2,$ and P$3-$of a gas corporation supply gasoline to three of their distributors located in the city at three different locations$-$A$,$ B$,$ and C$.$ The plants' daily capacities

are $4500,3000.$ and $5000,$ gallons, respectively, while the distributors' daily requirements are $5500,2500,$ and $4200$ gallons. The per$-$gallon transportation costs $($in $5)$ are provided in the

table below.

Because of a failure of expected supply earlier, the distributors $A,B,$ and C have decided to charge a penalty this time of $$0\mathrm{.}45,50\mathrm{.}55,$ and $50\mathrm{.}5$ per gallon, respectively, to avoid any

further delays.

FORMULATE A PROBLEM TO determine the optimum supply of gasoline to the distributors in order to minimize the total transportation cost as well as the charges payable as penalty.

SOLVE FOR THE PROBLEM IN EXCEL.