Armstrong Industries makes two different grades of steel at its plants in Midland and Donora. Weekly demand is at least 500 tons for grade 1 steel and at least 450 tons for grade 2. Due to differences in the equipment and the labor force, production times and costs per ton for each grade of steel differ slightly at each location, as shown in the following table.

Find the number of tons of each grade of steel that should be made each week at each plant so that Armstrong meets demand at minimum cost. Find the minimum cost.

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Grade 1 Grade 2 Furnace Min/ Cost/ Min/ Cost/ Time/Week Ton (in Minutes) 19,460 Ton Midland Ton Ton 40 $300 $330 45 $360 $270 Donora 44 21,380