The Calcio Coal Company produces coal at four mines and ships it to four power plants $($P$1-$P$4).$

The cost per ton of producing coal and the production capacity $($in tons$)$ for each mine are

known. The number of tons of coal demanded by each customer is also known. The cost $($in

dollars$)$ of shipping a ton of coal from a mine to each plant is available as well. The following

table provides the data:

Calcio wishes to minimize the cost of transporting coal from its mines to its plants. What is the minimum

cost$?$P$1$

P$2$

$133$

P$3$

P$4$ Capacity

Cost

Mine $1$

$9$

$15$

$8$

$10$

$125$

$50$

Mine $2$

$7$

$15$

$14$

$12$

$100$

$57$

Mine $3$

$5$

$5$

$11$

$12$

$150$

$55$

Mine $4$

$3$

$6$

$8$

$11$

$120$

$61$

Demands

$110$

$115$

$135$

$130$