Case Problem 5 DUKE ENERGY COAL ALLOCATION
1. Determine how much coal to purchase from each of the mining companies and how
it should be allocated to the generating units. What is the cost to purchase, deliver, and process
the coal?
2. Compute the average cost of coal in cents per million BTUs for each generating
unit (a measure of the cost of fuel for the generating units).
3. Compute the average number of BTUs per pound of coal received at each generating
unit (a measure of the energy efficiency of the coal received at each unit).
4. Suppose that Duke Energy can purchase an additional 80,000 tons of coal from
American Coal Sales as an “all or nothing deal” for $30 per ton. Should Duke
Energy purchase the additional 80,000 tons of coal?
5. Suppose that Duke Energy learns that the energy content of the coal from Cyprus Amax
is actually 13,000 BTUs per pound. Should Duke Energy revise its procurement plan?
6. Duke Energy has learned from its trading group that Duke Energy can sell 50,000
megawatt-hours of electricity over the grid (to other electricity suppliers) at a price
of $30 per megawatt-hour. Should Duke Energy sell the electricity? If so, which
generating units should produce the additional electricity?
Model:
Decision Variables
Let Xit = Tons of coal purchased from supplier i and used by generating unit t.
i=1(RAG), 2 (Peabody), 3(American),4(Consol),5(Cyprus),6(Addington),7(Waterloo)

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Chapter 4 / Exercise 27

**Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach**

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