The fuel distribution system of a small region contains four reserve tanks of fuel and three stations for selling fuel. There is a temporary shortage in the stations, which must be supplied from the reserve tanks. The reserve amounts, the shortage amounts, and the cost of transporting $1$ unit of fuel between a reserve tank and a station are the following.

Reserves:

Tank$-1$: $\mathrm{290}$ units

Tank$-2$: $\mathrm{230}$ units

Tank$-3$: $\mathrm{190}$ units

Tank$-4$: $\mathrm{190}$ units

Shortages $($note: their total is smaller than the total reserves$)$:

Station$-$A: $\mathrm{250}$ units

Station$-$B: $\mathrm{270}$ units

Station$-$C: $\mathrm{290}$ units

Transportation costs $($per unit of fuel$)$:

 Tank$-1$ Tank$-2$ Tank$-3$ Tank$-4$:

Station$-$A: $\mathrm{25}$$ $\mathrm{19}$$ $\mathrm{17}$$ $\mathrm{34}$$

Station$-$B: $\mathrm{29}$$ $\mathrm{23}$$ $\mathrm{18}$$ $\mathrm{32}$$

Station$-$C: $\mathrm{28}$$ $\mathrm{22}$$ $\mathrm{19}$$ $\mathrm{33}$$

$($a$)$ What is the minimum total transportation cost if all shortages are supplied from the reserve tanks?