An energy producing company (let’s call it “Pollution, Inc.”) owns two mines: Millborough and Lancaster. Each produces three different grades of coal: high, medium, and low. Millborough produces 3 tons of high-grade coal, 1 ton of medium-grade coals and 2 tons of low-grade coal during each operating hour. On the other hand, Lancaster produces 1 ton of high-grade coal, 1 ton of medium-grade coal and 4 tons of low-grade coal during each operation hour. It costs $1,500 for each operating hour at Millborough and only $1,000 for each operating hour at Lancaster. To supply enough coal for a local power plant, Pollution, Inc., needs to produce at least 16 tons of high-grade coal, 10 tons of medium-grade coal as well as 30 tons of low-grade coal per day.

What are the optimal number of operating hours for each plant to provide the most cost-effective solution for Pollution, Inc., to meet its obligations?

1) Formulate a complete linear programming model for this problem.

2) Use Excel’s Solver to find the optimal solution. How many hours should Millborough and Lancaster be operated, respectively? What is the overall cost?

3) Which are the binding constraints for this problem?

4) Include a screenshot of your answer report.