Future Plastics Manufactures Plastic Products for Industrial Use Worldwide

question 103

Multiple Choice

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million.
The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:
Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.
Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

-Max Z = 5x1 + 6x2
Subject to17x1 + 8x2 ? 136
    3x1 + 4x2 ? 36
    X1, x2 ? 0 and integer
What is the optimal solution?

• A) x1 = 6, x2 = 4, Z = 54
• B) x1 = 3, x2 = 6, Z = 51
• C) x1 = 2, x2 = 6, Z = 46
• D) x1 = 4, x2 = 6, Z = 56

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Definitions:

Anecdote

A short and interesting story or account of a real incident or event, often used to illustrate a point or entertain.

Experimental Result

The outcome or data obtained from conducting a systematic investigation in a controlled setting aimed at testing a specific hypothesis.

Selective Truth

The practice of presenting facts or data that only support one side of an argument while ignoring information that contradicts it.

Correlational Result

A statistical outcome indicating the degree to which two or more variables fluctuate together, but without implying causation between them.