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Future Plastics Manufactures Plastic Products for Industrial Use Worldwide

question 45

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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)
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)     -Which of these constraints will ensure that a low capacity facility is<i>not</i>built in South America? A)  Y12 + Y22 ? 1 B)  Y12 + Y22 =1 C)  Y12 + Y22 =0 D)  Y21 + Y22 ? 1
-Which of these constraints will ensure that a low capacity facility is not built in South America?


Definitions:

Rate of Return

The profit or deficit from an investment during a certain timeframe, represented as a portion of the investment's starting price in percentage terms.

Simple Interest

A financial term referring to a method of calculating the interest charge on a loan or investment based on the original principal amount, the interest rate, and the time the loan or investment is made for.

Guaranteed Investment Certificate

A secure investment that guarantees to return the principal plus interest at a specified rate over a fixed period.

Annual Interest Rate

The percentage of principal that is paid as interest to the lender annually, not accounting for the compound interest within that year.

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