Coal, Inc. has three mines. Coal from the three mines is transported to a central location where it is processed (in a single production run, using coal from all three mines together), and shipped to four customers.
The cost of producing coal, the ash and sulphur content per ton of coal, as well as the capacity of each mine and demand by each client are found in the worksheet. In addition, the cost of shipping from each mine to each client is also listed.
Quality requirements are such that ash cannot make up more than 6% of the total coal shipped to each customer, and sulphur cannot make up more than 3.5% of the total coal shipped to each customer. In the Excel file provided, build a linear programming model, then use Excel’s Solver add-in to determine how to minimise the cost of meeting customer demands.
Be sure to use the text-boxes within the Excel file to describe your objective function and constraints as indicated.
Based on the result of your optimisation model, what is the Total Cost, according to the optimal solution? Provide variables, objective, and, constraints before final answer.