Part 3 . A company owns three factories on the Washita River that emits four dif

Question

Part 3. A company owns three factories on the Washita River that emits four different pollutants. The state has recently mandated at least a 22 ton reduction for each pollutant. The company is considering the tonnage of emissions to process from each factory that will reduce the amount of pollutants in the river that meet state requirements for each pollutant. The company has available processes for each factory effective in reducing the pollutants but the cost and efficiency vary between factories as illustrated in the table. For example, one ton processed by Factory A will reduce pollutants 1,2,3,4 by 0.03, 0.04, 0.06, 0.02 tons respectively.

Tons Reduced per Ton Processed

Cost/Ton

Pollutant 1

Pollutant 2

Pollutant 3

Pollutant 4

Factory A

370

0.03

0.04

0.06

0.02

Factory B

280

0.02

0.05

0.04

0.03

Factory C

250

0.05

0.03

0.02

0.04

Question 8. What is the minimum cost that meets state requirements?

(A) $182500   (B) $181500   (C) $180500   (D) $183500   (E) none of the above

Part 4. An international distribution company of containers has operated a warehouse in Manila to service customers between the Asian continent and the North American continent for the past four years. Liann Able, VP of logistics, calls the planning meeting to order and begins discussion on the transportation plans to respond to recent changes in unit costs due to cost adjustments within the different countries. The unit costs of shipping from each source warehouse to each destination site, the capacity (in thousands) of the warehouses, and the demand (in thousands) of the destination sites are given in the table.

Unit

Customers

Costs

Tokyo

Shanghai

Hong Kong

Capacity

Warehouses

Vancouver

$21

$24

$26

200

Seattle

$20

$22

$21

180

San Francisco

$16

$13

$14

190

Los Angeles

$28

$27

$29

210

Demand

260

280

220

Question 9. What is the minimum total shipping cost in thousands that satisfies the requirements?

     (A) $9880   (B) $15940   (C) $10880   (D) $15620   (E) none of the above

Part 5. Burke Concrete Company produces concrete in a batch process. Each batch is 2000 tons. The dry ingredients are cement, sand, and gravel. The cement by weight makes up between 12% and 18% of a batch and costs $58.95 per ton. Sand by weight costs $12.95 per ton and must make up between 25% and 40% of a batch of the concrete. Gravel costs $10.95 per ton and must make up between 35% and 60% of the concrete. The amount of sand must never exceed gravel in a batch. Each daily production of 2,000 tons of concrete must contain exactly 93% of cement, sand, and gravel. Define X=tons of sand in each 2,000 ton batch, and Y=tons of gravel in each 2,000 ton batch.

Question 10. What is the optimal daily ingredient mix for Burke Concrete that minimizes cost?

Mix (A)

Mix (B)

Mix (C)

Mix (D)

(E) None of

the above

Tons of Cement

240

360

240

360

Tons of Sand

500

800

500

800

Tons of Gravel

700

700

1120

1200

Cost

28288

39247

32887

44722

Tons Reduced per Ton Processed

Cost/Ton

Pollutant 1

Pollutant 2

Pollutant 3

Pollutant 4

Factory A

370

0.03

0.04

0.06

0.02

Factory B

280

0.02

0.05

0.04

0.03

Factory C

250

0.05

0.03

0.02

0.04

Explanation / Answer

Part 3 : We need to have data related factory capacities to calculate total pollutant.

Question 8 : Answer is E). None of the above

Part 4 Question 9 : Answer is D) - $ 15620

We can solve the problem using LP and shown below:

Part 5 - Question 10: Data is missing in the given table (Last column).

Once we have missing information, problem can be solved using LP as shown in Part 4.

Tokyo Shanghai Hong Kong Capacity Vancouver 21 24 26 200 Seattle 20 22 21 180 San Francisco 16 13 14 190 Los Angeles 28 27 29 210 Demand 260 280 220 Tokyo Shanghai Hong Kong Vancouver 200 0 0 Seattle 60 0 120 San Francisco 0 90 100 Los Angeles 0 190 0 Constraints 200 <= 200 180 <= 180 190 <= 190 190 <= 210 260 = 260 280 = 280 220 = 220 Obj.Fun 15620

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