A gas supplier has three plants (i.e. P1, P2, and P3) supplying gasoline to three distributors 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 \$) are provided in the table below: Due to a failure of expected supply earlier, the distributors A,B, and C decided to charge a penalty of $0.45,$0.55, and $0.5 per gallon, respectively, to avoid any further delays. Determine the optimum supply of gasoline to the distributors to minimize the total transportation cost as well as the charges payable as penalty