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$?$