The Calcio Coal Company produces coal at four mines and ships it to four power plants (P1-P4). 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: Mine P1 P2 P3 P4 Capacity Cost 1 9 15 8 10 125 50 2 7 15 14 12 100 57 3 5 5 11 12 150 55 4 3 6 8 11 120 61 Demand 110 115 135 130     Problem 1: Transporting Coal Using the strategy that minimizes cost, how many tons of coal are shipped from Mine 4 to P1?

The Lead Zeppelin Company produces powered and steerable lighter-than-air craft. The company’s airships are specially lined and are therefore safer than normal dirigibles. The table below shows the weekly production of dirigibles, along with the associated Average Cost and Total Revenue figures (the Average Cost and Total Revenue figures are actually in thousands of dollars, so the $15 represents $15,000, but we have left off the zeros to save space).   Quantity Average Cost Total Cost Total Revenue 0  -- 0 $0 1 $15 15 $10 2 $9 18 $20 3 $8 24 $30 4 $8.50 34 $40 5 $9 45 $50 6 $10 60 $60 7 $12 84 $70   The Lead Zeppelin Company has decided that it will produce at least 1 dirigible. Now the question becomes, how many more dirigibles should it produce to make as much profit as possible?   Use the profit-maximizing rule to explain how many dirigibles the Lead Zeppelin Company should produce to…