Electric companies generate power from a number of different energy sources. Bumpton Power Co. uses coal, oil, gas, and nuclear power for generation. Their goal is to maximize their profit, but a number of factors restrain their generation of power.

Constraints
One constraint on the company is the limit on particulate pollution which they can release into the atmosphere. They are limited to 35200 lbs. per month of particulate pollution. Every gigawatt hour (gwh) of electricity generated by burning coal produces 100 lbs. of particulates. Oil produces 20 lbs. of particulates for each gwh of electricity generated, and natural gas produces 5 lbs. for each gwh. (Nuclear fuel does not involve combustion and therefore produces no particulates.)


The company also has restrictions placed on its sulphur dioxide (SO2) emissions. No more than 8800 lbs. of SO2 can be released into the atmosphere. The burning of coal releases 20 lbs. of SO2 for each gigawatt hour of electricity generated, burning oil produces 15 lbs. of SO2 for each gwh of electricity generated, and burning natural gas produces 3 lbs. of SO2 for each gwh of electricity generated. (Nuclear generation produces no SO2.)


Nuclear waste has no approved disposal mechanism. Because of this the company's use of nuclear energy is limited to production of no more than 330 gwh from nuclear energy.


Bumpton knows that it can sell no more than 880 gwh of electricity per month, so it limits its generation so as not to exceed that production level.


Coal and oil are hauled to the company site by train. Each gwh of power generated by burning coal requires 5 containers of coal, and each gwh of power generated from oil requires 2 containers of oil. The carrying capacity of the railroad track limits hauling to 2200 containers per month.


Generation of power using natural gas is limited by gas supply to no more than 220 gwh per month.
The company sells its electricity for $30,000 per gwh. However, this is by no means all profit. For each gwh of power generated by burning coal their fuel costs and operating costs are $12,000. For each gwh of power generated by burning oil their fuel costs and operating costs are $20,000. For each gwh of power generated by burning natural gas their fuel costs and operating costs are $24,000. And for each gwh of power generated by nuclear energy their fuel costs and operating costs are $26,000.



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The Problem
Your problem is to determine what fuel mix Bumpton Power Co. should use, and what the profit will be with that fuel mix.

Presumably you will want to do this problem with a good computer tool for doing matrix arithmetic. I suggest you use fractions rather than decimal numbers.

First, of course, you need to get the problem set up correctly. To set up your profit function, you'll need to use the fact that

Profit = Selling price - Costs

So, for example, the profit from selling a gwh of energy produced from coal would be $30,000 - $12,000 = $18,000.



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Use the following variable names:
x = # gwh produced by coal
y = # gwh produced by oil
z = # gwh produced by natural gas
w = # gwh produced by nuclear
Accuracy: Remember that WebAssign generally requires that answers be within around 1% of the correct answer. So your answers don't have to be exact in order to be scored as correct.
In your optimal solution, how many gwh of electricity are produced from burning coal?

How many gwh of electricity are produced from burning oil?

How many gwh of electricity are produced from burning natural gas?

How many gwh of electricity are produced from nuclear energy?

What is the maximum profit? (do not include $ sign in answer)

Does the particulate pollution constraint matter? (In other words, if this constraint were not in effect could the company make a larger profit?) ---Select--- Yes No

Does the sulphur dioxide constraint matter? ---Select--- Yes No

Does the nuclear waste disposal constraint matter? ---Select--- Yes No

Does the limited carrying capacity of the railroad track matter? ---Select--- Yes No

Does the limited natural gas supply matter? ---Select--- Yes No

2/14/2007 9:49:34 PM

im with you... dont have a clue.

[Edited on February 14, 2007 at 9:53 PM. Reason : 0]

2/14/2007 9:53:24 PM

Check your PM.

2/15/2007 11:27:19 AM