five different investments

The CFO of a department of a large Korporation evaluates five different investments ne. If it requires taken up, each investment a capital expenditure now and an additional capital expenditure in six months, with incomes produced twelve months in the future. E.G. project one requires an investment of $11 million now and $3 million produces six months from now on and $16 million tariff twelve months. The investments as well as their capital expenditure shown in table 4.3. ($26 million) and shown in six to spend now existing has quantities capital the CFO, months ($12 million) also in this table. Principal, which cannot now used is not spoken and in six months is invested, there these quantities are not assigned you to other projects under the area of application of the CFO. A project can be taken up in a partial amount at break costs, but in it produced also a break return. E.G. the CFO can decide to take to half a position in project 1 at costs $5,5 of million today and $1,5 of million into six months, but realise only a return of $8 million. From the five possible projects which positions, if the CFO lets order in, around the income of to maximise these projects one year therefore? We do not only have a problem, but we have also a model, because there are obviously described objectives, delimitations and assumptions.
There is an optimal solution, although we can see possibly not immediately, what it is. How do we find it? We could begin, by ordering the projects by the quantity of the income, which produce them and which maintenance, which uses takes up projects to the existing capital. Project 5 has the highest value, but notices that it requires the entire capital budget of $12 million available in six months. So if project 5 is taken up in its entireness, it the only project, which can be taken up, and which is produced incomes in twelve months you $40 million. Since the capital, which is present for investment in six months, is limited, its an alternative beginning to order the projects from few to the capital at most inside used like all it functions • 49 table 4.3 quantities in the millions dollar 1 capital 2 3 4 5 available invests income project produced after 12 months 16 16 15 14 40 - investment required now 11 10 5 5 10 26 investment required in 6 months 3 4 5 3 12 12 this period and projects, until the existing capital uses to hold to take up. Projects 1 and 4 in each order use the little head after six months, followed by projects 2, 3 and 5th noticing it that projects can be taken up 1, 4 and 2 in their entireness however together in them to use you all $26 million of the serious-existing now. However the combined income of these projects is million on increase $46 of $6 million over the preceding solution. Ours ad hoc approach seems to work, but there must be a better way. Even if we happen after an optimal solution, how we know them are optimal? Management scientists employ this difficulty, by converting first the model into mathematics. To do, beginning r by we a variable for each project present. For example, x1 could represent, to take up how much of the project 1 to. If x1 is 0, we do not take up you the project, if x1 is 1, we take up the project in its entirety 0_, and if x1 on a break value takes, we take up this break of the project n. With this variables, it is now possible to cause a mathematical model as in table 4.4. The expression on the right side of the word „“is the target function maximises, and it gives the income, which is connected with each possible solution. The remaining expressions represent you the delimitations n. If we select values for the variables, which satisfy these delimitations, then the appropriate choice can be taken up by projects. Likewise each possible project can be represented by a suitable choice by variables. The best solution, which we up to now found, represented as x1 = 1, x2 = 1, x3 = 0, x4 = 1 and x5 = 0. A use creation of a mathematical model is that it can be given to a computer. The computer understands the mathematical objective and the delimitations and can be explained to look for a solution. Does not interest it, where the objective and the delimitations of came. Knowing that the model is in this mathematical form it will look for, it you for an optimal solution. The methods computers you find understanding by those that optimal solutions requires a background in mathematics and management scientists dedicate considerable energy developing the ever better methods.
Giving the problem of the CFOS to a computer, we find that the optimal solution is x1 = 1, x2 = 3/4, x3 = 0, x4 = 1 and x5 = 1/4, with a connected income of $52 million. Many important lessons can be scholarly by this example. First it is not immediately free, why this is the optimal solution. We can examine that the solution satisfies the delimitations and that it has a value of $52 million, but why take up you 3/4 of project 2 and 1/4 of project 5? Unfortunately during we normally convince that the solution seems at least appropriate, can there