Three plants P$1,$ P$2,$ and P$3$ 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:

Distributor

Plant

A

B

C

P$1$

$0\mathrm{.}8$

$0\mathrm{.}5$

$1$

P$2$

$0\mathrm{.}7$

$0\mathrm{.}65$

$0\mathrm{.}8$

P$3$

$0\mathrm{.}5$

$0\mathrm{.}45$

$0\mathrm{.}7$

What is the optimal minimized cost?