Copperfield Mining Company owns two mines, each of which produces three grades of ore - high, medium, and low. The company has a contract to supply a smelting company with at least (and maybe more than) 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore during each hour it operates. Mine 1 produces 6 tons of high-grade ore, 2 tons of medium-grade ore, and 4 tons of low-grade ore per hour. Mine 2 produces 2 tons of high-grade ore, 2 tons of medium-grade ore, and 12 tons of low-grade ore per hour. It costs the company $200 per hour to operate mine 1 and it costs $160 per hour to operate mine 2. The company wants to determine the number of hours it needs to operate each mine so that it can meet its contractual obligations at the lowest cost.

1)What are the number of hours it needs to operate each mine so that it can meet its contractual obligations at the lowest cost and what is this lowest cost?

2)What is the meaning of the range of optimality for the cost contributions for the two decision variables in the context of the numbers

3)What is the meaning of the range of feasibility for the RHS of the constraints, including the limiting numerical values in Excel and also what are the dual values or shadow prices that are involved with each constraint.