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A company has budgeted 10 million dollars in capital expenditure over the next five year to acquire new fixed assets such as property, plants and equipment.

How can I solve the problem that the feasible region is bounded and there is precisely one optimal solution?

user8314628
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  • There isn't enough information to solve this problem. Firstly, what are you trying to optimize? How do the assets relate to the thing you are trying to optimize? Who are the investments in assets constrained (e.g. can there be negative investments in equipment, which might mean that equipment is sold)? – NicNic8 Feb 25 '19 at 02:51
  • @NicNic8 Sorry, these are all the information I have in the question. – user8314628 Feb 25 '19 at 02:53

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Presumably the variables will represent the amounts to be spent on the different possible assets. If all these have positive prices, the fact there is a fixed budget implies the feasible region must be bounded: if one unit of a particular asset has price $p$ and the total budget is $B$, you can't buy more than $B/p$ units of that asset. But you have told us nothing that would suggest there is only one optimal solution. It's perfectly possible, for example, that asset $x$ and asset $y$ are completely equivalent.

EDIT: Oh, is the question to design a linear programming problem? Well then, you could make up an objective and some constraints, including one that says the total amount spent on property, plants and equipment is at most $10$ million. With any luck, your problem will have a unique optimal solution. If it's not unique, change some coefficient.

Robert Israel
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