Three Plants P1, P2, and P3 of a Gas Corporation

Essay

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. 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 $) are provided in the table below.
​ $$\begin{array}{l}\begin{array} { l c c c } &\text { Distributor }\\\hline \text { Plant } & \text { A } & \text { B } & \text { C } \\\hline \text { P1 } & 0.8 & 0.5 & 1 \\\text { P2 } & 0.7 & 0.65 & 0.8 \\\text { P3 } & 0.5 & 0.45 & 0.7\end{array}\end{array}$$ ​
Because of a failure of expected supply earlier, the distributors this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively for the locations A, B, and C to avoid any further delays.
Find an alternative optimal solution for this transportation problem?