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?
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.