Today we rehearsed the allocation if you need a summary here it is!
I drove off. The allocation
are mathematical operations that enable the sharing of values \u200b\u200band proportion of data items. These mathematical operations will prove crucial in determining the share of costs incurred in the consortium works. The allocation can be basically five types: simple direct
Allocation;
distributed simple inverse
composed Direct Allocation;
composed Allocation inverse
Allocation mixed (simple and compound).
distributed simple direct.
The sum to be distributed will be divided in direct proportion to one set of data. We will indicate with S the sum to be distributed; shares distribution with X, Y, Z such quotas should be divided in direct proportion: x-a; ab Y, Z ac
It will set many shares as there are proportions of allocation:
S: (a + b + c) = X: S
to: (a + b + c) = Y: b
S: (a + b + c) = Z: c
As you can see the first part of each proportion is the same and this is called a fixed quotient. For the fundamental property of aspect ratio (the product of the average is equal to the product of the extremes):
X = S (a + b + c) to
* Y = S: (a + b + c) * b
Z = S: (a + b + c) * c
is equivalent to multiplying the quotient fixed making it possible for data sharing.
Qf Qf
X * a = * b = Y c = Z * Qf
Logically X + Y + Z = S.
eg four owners of land adjacent farms (and similar surface) decide intrapoderale the construction of a road that links them to market more quickly and easily. The cost of 50 million pounds will be divided in direct proportion to the length of the stretch of road used by each landowner.
The owner uses X 260 m, the owner uses Y 320 meters, the owner uses Z 390 m, the owner uses 450 W m Determine the shares of expenditure due to each owner.
Qf = 50000000 / (260 + 320 + 390 + 450) X
Owner: Qf * 250 = £ 9,154,930
Owner Y: QF * 320 = £ 11,267,605
Owner Z: QF * 390 = £ 13,732 .395 W
Owner: Qf * 450 = £ 15,845,070
Logically, the sum of the shares of expenditure due to the various landowners will be £. 50,000,000
distributed simple reverse.
The sum to be distributed will be divided into a inversely proportional to a single set of data. S denote the sum to be distributed with X, Y and Z shares allocation, allotment in that X is divided in inverse proportion to a, Y will be divided in inverse proportion ab, Z will be divided in inverse proportion, and c .
take the reciprocal of the data problem, we transform the division into simple direct, so the quotient will be fixed:
Qf = S / (1 / a +1 / b +1 / c), multiplying by the reciprocal of the Qf data making it possible the division, you will get the shares allocation:
Qf * 1 / a = X
Qf * 1 / b = Y
Qf * 1 / c Z =
Logically, as detto per il riparto semplice diretto, la somma delle quote di ripartizione deve coincidere con la somma da ripartire, ovvero: X + Y + Z = S
p.e. quattro allevatori decidono la costruzione di un pozzo per abbeverare il bestiame al pascolo. Il costo per la costruzione del pozzo ammonta a £50.000.000 che verrà suddiviso in maniera inversamente proporzionale alla distanza media di ciascun pascolo dal pozzo stesso. Il pascolo del primo proprietario dista 230 m; il secondo dista 350 m; il terzo 540 m; il quarto 270 m.
Determinare le quote di spesa spettanti a ciascun proprietario fondiario.
Il Quoziente fisso sarà: 50.000.000 / (1/230+1/350+1/540+1/270)
Il primo allevatore pagherà: Q.f.* 1/230 = £. 17036235;
the second keeper: Qf * 1 / 350 = £. 11195240;
the third keeper: Qf * 1 / 540 = £. 7,256,175;
the fourth keeper: Qf * 1 / 270 = £. 14,512,350.
The sum of the allocation will be: £. 50,000,000
Direct Allocation compound.
The sum to be distributed will be divided in direct proportion to two or more data series. S denote the sum to be distributed with X, Y and Z-sharing quotas, in this division:
X will be divided in direct proportion to ael;
Y will be divided in direct proportion abem;
Z will be divided in direct proportion ace m.
the quotient will be fixed: S / (l + a * b * c * m + n), as already seen for other forms of allocation:
Qf * (a * l) = X +
Qf * (b * m) = Y +
Qf * (c * n) = Z =
Logically: S = X + Y + Z
eg four owners of farms adjacent to decide intrapoderale the construction of a road that links them to the market more easily. The cost of 50 million pounds will be divided not only a direct proportion to the length of the stretch of road used by each owner, but also to the surface of each fund.
The first owner has used 150 m sup. 15:40:30;
the second owner uses me has 230 sup. 30/08/1990;
the third owner uses me has 360 sup. 25.90.80;
the fourth owner uses me has 470 sup. 9.90.50.
determine the share of expenditure of each landowner.
Qf = 50000000 / (150 * 15.403 * 25.908 +230 +360 +470 * 8.309 * 9.905) The first owner will pay
: Qf * (150 * 15.403) = £. 6,346,080;
the second owner will pay: Qf * (230 * 8.309) = £. 5,249,110;
the third owner will pay: Qf * (360 * 25.908) = £. 25618020;
the fourth owner will pay: Qf * (470 * 9.905) = £.
The sum of 12,786,790 shares of breakdown is: £. 50,000,000
Allocation compound reverse.
The sum to be split will be distributed in inverse proportion to two or more data series. S denote the sum sa start, X, Y and Z-sharing quotas, in this allocation:
X will be divided in inverse proportion to ael;
Y will be divided in inverse proportion abem;
Z will be divided in inverse No proportional ace
take the reciprocal of the data making it possible the division, the division will turn composed of composite reverse direct. So Qf = S / (1 / (a \u200b\u200b* l) +1 / (b * m) +1 / (c * n))
Qf * 1 / (a \u200b\u200b* l) = X +
Qf * 1 / (b * m) = Y +
Qf * 1 / (c * n) = Z =
Logically: S
Four owners of farms adjacent to presenting a periodic stream flooding decided to build a dam to protect them from water. Spending on construction of the bank amounted to £ 50,000,000 and will be divided in inverse proportion to both the average distance of each farm from the bank than its average share over the level of the stream. The first company is 230
me share has 0.5 m;
the second largest is 320 m and 1 m this installment, the third company
me this installment is 310 m 0.75;
the fourth farm is 450 m and 0.25 m altitude has
Determine the share of expenditure due to each landowner.
Qf = 50,000,000 / (1 / (230 * 0.5) +1 / (320 * 1) +1 / (310 * 0.75) +1 / (450 * 0.25)) The first owner
pay: QF * 1 / (230 * 0.5) = £. 17383920;
the second owner will pay: QF * 1 / (320 * 1) = £. 6,247,345;
the third owner will pay: QF * 1 / (310 * 0.75) = £. 8,598,500;
the fourth owner will pay: QF * 1 / (450 * 0.25) = £. 17,770,235.
The sum of the allocation will be: £. 50,000,000
Allocation misto.
Per semplicità verrà trattato il solo riparto misto semplice. In detto riparto la somma da ripartire verrà suddivisa in maniera direttamente proporzionale ad una sola serie di dati ed in maniera inversamente proporzionale ad un'altra sola serie di dati. Indicando con S la somma da ripartire, con X, Y e Z le quote di ripartizione, in detto riparto:
X verrà suddiviso in maniera direttamente proporzionale ad a ed in maniera inversamente proporzionale ad l;
Y verrà suddiviso in maniera direttamente proporzionale a b ed in maniera inversamente proporzionale ad m;
Z verrà suddiviso in maniera direttamente proporzionale a c ed in maniera inversamente proporzionale ad n.
Interpolando fra loro i due tipi di riparti semplici visti si otterrà la soluzione di detto riparto:
Q.f. = S / ((a/l)+(b/m)+(c/n))
Q.f.* (a/l) = X+
Q.f.* (b/m) = Y+
Q.f.* (c/n) = Z=
Logicamente: S
p.e. quattro Comuni decidono la costruzione di un ponte che li colleghi più agevolmente alla rete viaria. La spesa di £50.000.000 (al netto del contributo statale) verrà suddivisa in proporzione diretta al numero di abitanti ed in proporzione inversa alla distanza media di ciascun Comune dal ponte.
Il primo Comune presenta 2.560 abitanti e dista 2,5 km;
il secondo Comune presenta 1.560 abitanti e dista 5,3 km;
il terzo Comune presenta 4.890 population and is 4.8 km;
the fourth municipality has 3,980 inhabitants and is 6.7 km: Determine
shares allocation of expenditure between the various municipalities.
Qf = 50,000,000 / ((2,560 / 2.5) + (1,560 / 5.3) + (4,890 / 4.8) + (3,980 / 6.7)) The first
City will pay: Qf * (2,560 / 2.5) = £. 17467730;
City will pay the second: Qf * (1,560 / 5.3) = £. 5,020,940;
the third largest municipality will pay: Qf * (4.890/4.8) = £. 17378175;
the fourth municipality will pay: Qf * (3,980 / 6.7) = £. 10,133,155.
As can be seen that the combined shares of distribution coincides with the sum to be divided: £. 50.000.000
This key feature of the allocation makes them difficult to associate with the type of problems errabili. With the completion of the problems relating to the allocation can be considered concluded the theoretical study of the entire financial mathematics (or not) that can be used in the formulation of the main analytical estimates that the future expert may use the estimated in practice. Estimative solvable problems are then dealt with the few known and mathematical formulas that show how the use of financial mathematics applied to such cases can lead to credible results. Indeed, rather than the outcome, will have the computing power demonstrated by the operator to which it is anticipated that the approximations value will not be carried out and found that the descriptive part, which is crucial in any kind of estimate, will be treated elsewhere.
source: http://www.istruzioneonline.it/archivio/estimo/3estimo2.htm
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