# Mplex vraagstuk lineair programmeren (?)

### #1

Mienzelf

Mienzelf

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Geplaatst op 10 september 2007 - 12:23

Hieronder treft u een opgave aan die ik voor mijn opleiding zal moeten oplossen. Wat ik al weet is dat er 18 variabelen te onderkennen zijn en evt. gebruik van 2 hulpvariabelen. Wie o wie weet welke dat zijn? Zelf kom ik slechts aan 12 stuks. Zie onderaan: max. winst dient uiteindelijk te worden berekend. Alvast bedankt!

DEEPDOWN MINES CORPORATION

Deepdown Mines Corporation (DMC) operates a strip coal-mining operation in western Pennsylvania. Three mines sites (A, B, and C) currently are used, each producing coal of somewhat different sulfur and ash content. Coal from these sites is transported to a common crusher that grinds the coal into a finer mix. The coal is then "washed" to remove some of the sulfur and ash. In the washing process, the crushed coal is fed into a large tank containing a fluid. The cleaner coal floats and is removed for sale. Coal containing a heavier concentration of impurities sinks to the bottom and is discarded.

By using washing fluids of different densities (that is, having differing specific gravities), the amount of impurities removed can be controlled. Three fluids are currently in use, called here Light, Medium, and Heavy. With the Heavy fluid, a greater percentage of the coal is recovered (i.e., floats), but a smaller percentage of the impurities is removed. Refer to Exhibit 1. For example, if the coal from mine A is washed using Light fluid, only 40 percent of the coal is recovered for sale. This recovered coal contains 0.62 percent sulfur and 1.6 percent ash. On the other hand, the use of Heavy fluid increases the yield to 55 percent, but the recovered coal contains 1.04 percent sulfur and 2.1 percent ash.

The crushing and washing operation is set up so that any combination of coal from any of the mines can be used in conjunction with any of the fluids . After the washing operation, all the recovered coal is mixed to make one blend, sold by DMC. Environmental requirements limit the blend to a maximum of 0.5 percent sulfur and 2.0 percent ash.

There are some other restrictions. The equipment available limits the amount that can be produced in each mine. See Exhibit 2. The crusher can handle a maximum of 8,000 tons per week of unwashed coal in regular time, but can be worked overtime up to an additional 4,000 tons. The cost of the crushing operation is \$5 per ton of unwashed coal in regular time and \$7.50 per ton on overtime. The washing tank can handle up to 6,000 tons of recovered coal on regular time and an additional 3,000 tons on overtime. The cost of washing is \$10 per ton of recovered coal on regular time and \$15 on overtime.

The variable costs of operating each mine are also shown in Exhibit 2. In addition, it costs \$2 per ton of unwashed coal for Light fluid, \$4 per ton of unwashed coal for medium fluid, and \$6 per ton of unwashed coal for Heavy fluid. DMC sells its coal blend for \$100 per ton.

Questions

Determine an optimal way to produce the coal blend. What is the profit gain of DMC if they do allow overtime compared to the situation without overtime?

Exhibit 1. Effects of different fluids on coal recovery and impurities remaining.

Mine Source and
Fluid Type Tons of Coal recovered per ton input Percent Sulfur content
of recovered Coal Percent Ash content
of recovered Coal
Mine A
Light 0.40 0.62 1.6
Medium 0.50 0.91 1.9
Heavy 0.55 1.04 2.1
Mine B
Light 0.70 0.22 1.9
Medium 0.90 0.35 2.3
Heavy 0.95 0.47 2.5
Mine C
Light 0.62 0.42 1.5
Medium 0.75 0.50 1.8
Heavy 0.82 0.78 2.2

Exhibit 2. Costs and capacities of DMC Mines.

Mine Capacity
(maximum tons mined per week) Cost
(\$ per ton mined)
A 6 000 25
B 2 300 45
C 5 000 40

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### #2

Bart

Bart

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Geplaatst op 10 september 2007 - 17:20

Als je nu eerst eens aangeeft welke variabelen je gevonden hebt. We zijn hier immers geen huiswerkmachine.
If I have seen further it is by standing on the shoulders of giants.-- Isaac Newton

### #3

Bart

Bart

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Geplaatst op 10 september 2007 - 17:21

Dit onderwerp past beter in het huiswerkforum en is daarom verplaatst.
If I have seen further it is by standing on the shoulders of giants.-- Isaac Newton

### #4

Mienzelf

Mienzelf

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Geplaatst op 10 september 2007 - 19:22

Hierbij de tabellen zoals ze moesten zijn.
Als variabelen heb ik zelf gevonden de 3x3=9 verschillende vloeistoffen, de 3 mijnen, crushed en washed. Ik zou dan een aparte berekening uitvoeren voor de overtime berekening, vervolgens de 2 uikomsten profits vergelijken.

```Exhibit 1. Effects of different fluids on coal recovery and impurities remaining.

Mine Source
and Fluid Type	Tons of Coal recovered per ton input		 Percent Sulfur content	Percent Ash content
of recovered			  of recovered Coal
Mine A
Light 					0.40											0.62					 1.6
Medium					0.50											0.91					 1.9
Heavy					 0.55											1.04					 2.1

Mine B
Light					 0.70											0.22					 1.9
Medium					0.90											0.35					 2.3
Heavy					 0.95											0.47					 2.5

Mine C
Light					 0.62											0.42					 1.5
Medium					0.75											0.50					 1.8
Heavy					 0.82											0.78					 2.2

Exhibit 2. Costs and capacities of DMC Mines.

Mine Capacity
(maximum tons mined per week)			  Cost (\$ per ton mined)
A	6 000								 25
B	2 300								 45
C	5 000								 40```

### #5

Mienzelf

Mienzelf

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Geplaatst op 10 september 2007 - 19:37

Hierbij de tabellen zoals ze moesten zijn.
Als variabelen heb ik zelf gevonden de 3x3=9 verschillende vloeistoffen, de 3 mijnen, crushed en washed. Ik zou dan een aparte berekening uitvoeren voor de overtime berekening, vervolgens de 2 uikomsten profits vergelijken.
In bijlage evt. de vraag in Word. Ik hoop dat iemand het kan uitleggen!

```Exhibit 1. Effects of different fluids on coal recovery and impurities remaining.

Mine Source
and Fluid Type	Tons of Coal recovered per ton input	Percent Sulfur content 	Percent Ash content
of recovered			  of recovered Coal
Mine A
Light 					0.40											0.62					 1.6
Medium					0.50											0.91					 1.9
Heavy					 0.55											1.04					 2.1

Mine B
Light					 0.70											0.22					 1.9
Medium					0.90											0.35					 2.3
Heavy					 0.95											0.47					 2.5

Mine C
Light					 0.62											0.42					 1.5
Medium					0.75											0.50					 1.8
Heavy					 0.82											0.78					 2.2

Exhibit 2. Costs and capacities of DMC Mines.

Mine Capacity
(maximum tons mined per week)			  Cost (\$ per ton mined)
A	6 000								 25
B	2 300								 45
C	5 000								 40```

****, tabel verschuift steeds. Zie bijlage voor de goede tabel.

Bijlage..

#### Bijgevoegde Bestanden

Veranderd door Mienzelf, 10 september 2007 - 19:37

### #6

Fred F.

Fred F.

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Geplaatst op 20 september 2007 - 15:47

@Mienzelf
Is een reactie op dit topic nu nog van belang of ben je er inmiddels zelf al uit?
Hydrogen economy is a Hype.

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