Working Example

Note: This example is just for demonstration purposes. This app comes pre-loaded with some example data which you can delete and then add your own friends and gifts.

Meet Hercules!

Hercules has 7 friends for which he would like to buy presents:

 

First he begins by scouring the Internet in order to find presents for them. He creates his gift basket and fills it with the following twelve gifts:

Gift #	Picture	Gift Name	Price		Gift #	Picture	Gift Name	Price		Gift #	Picture	Gift Name	Price
1		Apple Bunch	9.99		5		Pear	4.99		9		Redcurrant	4.50
2		Apple Duet	2.99		6		Pink Flower	19.99		10		Water Lily	39.99
3		Cherry	14.99		7		Plum	6.50		11		White Daffodil	28.95
4		Hay	24.99		8		Pumpkin	1.50		12		Yellow Daffodil	30.50

He then assigns preferences to each of his friends and preferences for each gift:

Friend #	Image	Friend	Overall Preference		Gift Preference
				Apple Bunch	Apple Duet	Cherry	Hay	Pear	Pink Flower	Plum	Pump- kin	Red- currant	Water Lily	White Daffodil	Yellow Daffodil
1		Racoon Boy	90	100	65	5	0	0	0	0	0	0	0	0	0
2		Moo Coo	35	0	0	0	100	0	0	0	0	0	0	0	0
3		Happy Hen	65	0	0	0	0	75	0	50	20	95	0	0	0
4		Piggy Pal	70	25	25	90	0	25	0	25	25	25	0	0	0
5		Dino Rex	30	0	0	75	0	0	50	0	0	0	40	45	40
6		Big Ted	60	0	0	0	0	0	0	0	0	0	100	60	80
7		Little Ted	80	0	0	0	0	0	40	0	0	0	75	65	100

Now he is able to begin his optimization. He starts by setting a maximum budget of 99,999.99:

Budget	Apple Bunch	Apple Duet	Cherry	Hay	Pear	Pink Flower	Plum	Pumpkin	Redcurrant	Water Lily	White Daffodil	Yellow Daffodil	Amount Spent
Price	9.99	2.99	14.99	24.99	4.99	19.99	6.50	1.50	4.50	39.99	28.95	30.50
Target 99,999.99													144.95
For an unlimited budget, everyone gets their favourite item. Except for Dino Rex who wanted Cherry. Unfortunately these have already been allocated to Piggy Pal who has a higher Overall Preference. Hence Dino Rex is allocated the Pink Flower which is his second favourite item.
144													131.46
As the budget is reduced, those with a lower Overall Preference are examined first and allocated their next favourite preference. However, as in this case, White Daffodil is Dino Rex next favourite item but this would break the budget constraint. Hence the allocation of Plum is the next cheaper and available item.
131													126.46
126													106.46
106													104.46
104													99.46
99													86.46
86													84.46
84													82.91
82													79.46
79													72.97
72													69.46
69													67.91
67													65.97
65													58.95
58													55.46
55													45.46