Min .8A + .6B
st:
12A + 3B >= 30
4A + 8B >= 24
A, B >= 0
[go back] [any Questions?]
Max 2x1 + 3x2st:
3x1 + x2 >= 6
x1 + 7x2 >= 7
x1 + x2 <= 4
x1, x2 >= 0
c) three extreme points:
point A : x1 = 1; x2 = 3
point B : x1 = 7/4; x2 = 3/4
point C : x1 = 3 1/2; x2 = 1/2
[go back] [any Questions?]
max 6x1 + 2x2st:
(1) 2x1 + 4x2 <=20
(2) 3x1 + 5x2 >= 15
(3) x1 >= 3
x2 >= 0
b) slack/surplus variables:
s1 = 0 (slack)
s2 = 15 (surplus)
s3 = 7 (surplus)
Formulation of the Foreign Exchange Problem
MAX Y1 + 1.42699 Y2 + 0.1236 Y3 + 0.37998 Y4 + 0.00444 Y5
SUBJECT TO
Y1 = 2 + 1.425 X21 + 0.1234 X31+ 0.3793 X41 + 0.00443 X51 - X12 - X13 - X14 - X15
Y2 = 5 + 0.6998 X12 + 0.08647 X32 + 0.2662 X42 + 0.0031 X52 - X21 - X23 - X24 - X25
Y3 = 0 + 8.078 X13 + 11.55 X23 + 3.073 X43 + 0.03586 X53 - X31 - X32 - X34 - X35
Y4 = 3 + 2.627 X14 + 3.754 X24 + 0.325 X34 + 0.01163 X54 - X41 - X42 - X43 - X45
Y5 = 0 + 224.7 X15 + 320.7 X25 + 27.76 X35 + 85.51X 45 - X51 - X52 - X53 - X54
Y3 >= 8
Y5 >= 1280
All XIJ and YI >= 0
Notes:
- For each currency i, Yi represents the final holding in millions of the denomination of the currency. For instance Y1 is final dollar holding (in dollars) Y2 is final pound holding (in pounds). Xij is millions of currency i exchnaged into currency j ( measured in i's denomination). For instance, X23 is millons of pounds exchanged into francs.
- The objective function evaluates the dollar worth of the final holding of all currencies. For instance each dollar is worth a dollar so the coeefficient of Y1 is 1 while each pound is worth $1.42699 (average of the 'bid' and 'ask' prices of pounds).
- For each currency there is an equation to express the final holding as the beggining amount plus all other currencies changed into this currency minus this currency changed into other currencies. For instance: Y2 is final holding of pounds. It starts with 5 million pounds, adds to it e. g., 0.6998 X12 ( pounds obtained as a result of exchanging X12 dollars) and likewise adds for other currencies exchanged into pounds. It then subtracts e.g., X21 (pounds exchanged for dollars) and likewise for other currencies bought using pounds.
- Y3>=8 and Y5>= 1280 require that we end up at least with the required amounts of these currencies, while Yi>=0 for other currencies require that we exchange at most the amount of surplus we have of these curencies.