Table 10-1 a Company Has Decided to Use 0-1 Integer Programming to Programming

question 21

Multiple Choice

Table 10-1
A company has decided to use 0-1 integer programming to help make some investment decisions.There are three possible investment alternatives from which to choose,but if it is decided that a particular alternative is to be selected,the entire cost of that alternative will be incurred (i.e. ,it is impossible to build one-half of a factory) .The integer programming model is as follows:
Maximize 5000 X₁ + 7000X₂ + 9000X₃
Subject to: X₁ + X₂ + X₃ ≤ 2 (only 2 may be chosen)
25000X₁ + 32000X₂ + 29000X₃ ≤ 62,000 (budget limit)
16 X₁ + 14 X₂ + 19 X₃ ≤ 36 (resource limitation)
all variables = 0 or 1
where X₁ = 1 if alternative 1 is selected,0 otherwise
X₂ = 1 if alternative 2 is selected,0 otherwise
X₃ = 1 if alternative 3 is selected,0 otherwise
The optimal solution is X₁ = 0,X₂ = 1,X₃ = 1
-In Table 10-1,which presents an integer programming problem,using the optimal solution means only two of the alternatives would be selected.How much slack is there in the third constraint?

• A)0
• B)3
• C)33
• D)36
• E)None of the above

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Definitions:

Marginal Private Cost

The cost incurred by a firm or individual resulting from producing one more unit of a good, excluding externalities or effects on third parties.

External Benefits

External benefits refer to the positive effects or advantages that a product or activity imparts on individuals or society who are not directly involved in the production or consumption of the good.

Network Externalities

The effect on a user of a product or service that results from an increase in the number of other users of the same or compatible products or services.

Natural Monopolies

Market conditions where a single firm can supply a good or service more efficiently than any competitor due to economies of scale, hence dominating the market.