Question: Anglo produces iron ore at three mining sites: A, B, and C. Mine A produces limonite ore with 65% iron content. It costs $360 and 4 labor hours to mine a ton of limonite ore at Mine A. Mine B produces limonite ore with 80% iron content. It costs $420 and 5 labor hours to mine a ton of limonite ore at Mine B. Mine C produces limonite ore with 50% iron content. It costs $240 and 3 labor hours to mine a ton of limonite ore at Mine C. Every month, Anglo has a total of 2500 labor hours available to allocate to these sites, and it can mine at most 250 tons from A, 200 tons from B, and 100 tons from C. Anglo has two customers: Vale and Fortescue. Vale has a monthly limonite ore demand of 260 tons, and it only purchases ore from mining sites with at least 60% iron content. Fortescue has a monthly limonite ore demand of 220 tons, and it purchase Anglo’s ore only from mining sites B and C. Fortescue requires that no more than 25% of its ore come from site C. Anglo wants to satisfy all of its customers’ monthly demand while minimizing its cost.

a. Formulate a linear programming model to determine Anglo’s production plan. [15%]

b. Solve the model using Excel Solver. [5%]

c. Consider the optimal solution Excel found in part b.

i. Do any of the mines have slack capacity? If yes, which ones? [2%]

ii. What would the effect be on the current optimal solution if Anglo can mine at most 230 tons from A in every month? (Increase or decrease by how much? Or no change? Why?) [2%]