MINERVA superseeded IF/Prolog.
Please see
http://www.ifcomputer.co.jp/MINERVA
for details.
We discontinued to sell IF/Prolog Dec 31. 2003.
For current customers, we continue to provide
professional support for IF/Prolog until Dec 31, 2008.
The treasurer has forecast the cash needs for the next 5 years.
He has cash requirements of 10000 at the beginning of each of the
first 2 years and 20000 at the beginning of the remaining 3 years.
The treasurer is considering the following investments:
- intermediate bonds have a return, after 2 years, of 1.47 for each
1.00 invested.
- long-term bonds have a return, after 3 years, of 1.78 for each
1.00 invested.
- short-term bonds have a return, after 1 year, of 1.20 for each
1.00 invested.
1. Supposing the corporation currently has 100000 available cash, the
treasurer wishes to maximize the amount of cash at the end of the
planning period, at which time no investment will be outstanding.
?- cash(100000, Out), linear_maximize(Out, Max).
Max = 0r18297283/147 = 124471
2. Using the same model, determine the minimal start capital necessary
to meet the cash requirements.
?- cash(In, _), linear_minimize(In, Min).
Min = 0r100833685000/1923201 = 52430
3. Using the same model, determine the minimal start capital the company
must have in order to have at the end of the planning period the same
amount of cash (while meeting the cash requirements during the 5 years).
?- cash(In, In), linear_minimize(In, Min).
Min = 0r100833685000/1188201 = 84862
:- module(cash).
:- export([cash/3]).
:- begin_module(cash).
:- import(const_linear).
cash(In, Out1) :-
V = [ In, C1, C2, C3, C4, Out,
Profit1, Profit2, Profit3, Profit4, Profit5,
I1, I2, I3, I4, I5,
I11, I12, I13,
I21, I22, I23,
I31, I32, I33,
I41, I42,
I51
],
all_positive(V),
C1 + 10000 + I1 $= In + Profit1,
C2 + 10000 + I2 $= C1 + Profit2,
C3 + 20000 + I3 $= C2 + Profit3,
C4 + 20000 + I4 $= C3 + Profit4,
Out + 20000 + I5 $= C4 + Profit5,
I1 $= I11 + I12 + I13,
I1 + 10000 $=< In,
Profit1 $= I11 * 0r120/100,
I2 $= I21 + I22 + I23,
I2 + 10000 $=< C1,
Profit2 $= I21 * 0r120/100 + I12 * 0r147/100,
I3 $= I31 + I32 + I33,
I3 + 20000 $=< C2,
Profit3 $= I31 * 0r120/100 + I22 * 0r147/100 + I13 * 0r178/100,
I4 $= I41 + I42,
I4 + 20000 $=< C3,
Profit4 $= I41 * 0r120/100 + I32 * 0r147/100 + I23 * 0r178/100,
I5 $= I51,
I5 + 20000 $=< C4,
Profit5 $= I51 * 0r120/100 + I42 * 0r147/100 + I33 * 0r178/100,
linear_maximize(Out,Out1),
write(V).
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