Combinations with Best Total value without Exceeding a maximum cost

Hello,
I have an interesting problem I am trying to solve and I am wondering if TSQL, or another tool like SSAS would be a good option for this. I am trying to find out the best performance from 8 parts while staying under a specific budget. Below is a generic
example:
I have to find the best combination of the following:
3 Part A
3 Part B
1 Part C
1 Part D(can be either A, B, or C)
The raw data that I will be using will look something like this:
Part #  |  Price   |  Value  | ID
A          |  $22     |  44      |   1
A          |  $21     |  42      |   2
B          |  $20     |  41      |   3
C          |  $18     |  37      |   4
B          |  $17     |  35      |   5
B          |  $2       |  1        |   200
I will have over 200 combinations of parts in total (some A, some B, some C).
In addition, I will have to find the best optimal total value for 100$ or less. It will be like Use it or Lose it 100$ so you want to be as close as possible without going over. 
I am looking for something that can find out the optimal and rank it according to total value in a relatively quick amount of time. I know there are a lot of possibilities for this.
The end result will be something like this:
Total Value | Total Cost | A1 | A2 | A3 | B1 | B2 | B3 | C1 | D1
240           |   100        | 1  |  6 |  15 | 2  |  5 | 20 |  4 |  3
Let me know if you have any questions. Hopefully this makes some sense.

CREATE TABLE [dbo].[OptimalCombo](
[ID] [float] NULL,
[Price] [money] NULL,
[Value] [float] NULL,
[Part] [nvarchar](255) NULL,
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('1',convert(money,'22.16'),'42.7302','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('2',convert(money,'21.67'),'42.0798','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('3',convert(money,'20.42'),'40.7089','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('4',convert(money,'16.05'),'34.4474','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('5',convert(money,'11.66'),'33.9312','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('6',convert(money,'18.27'),'33.7518','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('7',convert(money,'18.57'),'32.5026','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('8',convert(money,'13.64'),'32.0993','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('9',convert(money,'15.16'),'31.8969','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('10',convert(money,'11.87'),'31.6139','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('11',convert(money,'15.22'),'31.3825','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('12',convert(money,'18.77'),'31.2071','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('13',convert(money,'12.96'),'31.1526','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('14',convert(money,'14.22'),'30.2834','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('15',convert(money,'14.57'),'30.2159','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('16',convert(money,'14.89'),'30.1422','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('17',convert(money,'15.42'),'30.0975','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('18',convert(money,'15.26'),'29.9128','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('19',convert(money,'10.87'),'29.5804','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('20',convert(money,'12.38'),'29.0499','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('21',convert(money,'15.23'),'28.8299','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('22',convert(money,'12.87'),'28.8112','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('23',convert(money,'17.05'),'28.6106','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('24',convert(money,'14.62'),'28.4499','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('25',convert(money,'11.71'),'28.4443','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('26',convert(money,'13.84'),'27.4249','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('27',convert(money,'14.68'),'27.1489','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('28',convert(money,'11.50'),'27.0866','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('29',convert(money,'12.69'),'27.0484','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('30',convert(money,'12.51'),'27.0121','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('31',convert(money,'14.02'),'26.4007','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('32',convert(money,'13.61'),'26.0659','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('33',convert(money,'10.31'),'25.1806','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('34',convert(money,'13.62'),'24.8248','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('35',convert(money,'13.42'),'24.6756','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('36',convert(money,'11.82'),'24.4752','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('37',convert(money,'10.95'),'24.0582','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('38',convert(money,'14.26'),'23.4754','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('39',convert(money,'9.62'),'23.4578','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('40',convert(money,'9.80'),'23.3932','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('41',convert(money,'7.91'),'22.7474','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('42',convert(money,'9.96'),'22.5954','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('43',convert(money,'9.13'),'22.2856','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('44',convert(money,'13.54'),'22.2192','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('45',convert(money,'11.01'),'21.8734','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('46',convert(money,'9.06'),'21.809','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('47',convert(money,'10.56'),'21.7806','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('48',convert(money,'10.10'),'21.5777','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('49',convert(money,'9.17'),'21.5588','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('50',convert(money,'8.31'),'21.4629','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('51',convert(money,'8.66'),'20.9096','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('52',convert(money,'12.33'),'20.7805','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('53',convert(money,'12.18'),'20.7249','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('54',convert(money,'10.90'),'20.7121','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('55',convert(money,'9.66'),'20.6709','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('56',convert(money,'10.14'),'20.5873','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('57',convert(money,'10.11'),'20.5527','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('58',convert(money,'11.63'),'20.5245','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('59',convert(money,'8.91'),'20.3243','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('60',convert(money,'7.33'),'19.9983','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('61',convert(money,'12.44'),'19.9376','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('62',convert(money,'10.39'),'19.8531','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('63',convert(money,'9.49'),'19.7441','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('64',convert(money,'10.41'),'19.54','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('65',convert(money,'9.28'),'19.4863','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('66',convert(money,'9.93'),'19.3653','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('67',convert(money,'10.63'),'18.7178','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('68',convert(money,'8.73'),'18.7176','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('69',convert(money,'8.77'),'18.6663','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('70',convert(money,'6.81'),'18.4952','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('71',convert(money,'9.34'),'18.4944','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('72',convert(money,'10.93'),'18.3211','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('73',convert(money,'0.00'),'18.0332','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('74',convert(money,'10.09'),'17.5418','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('75',convert(money,'6.46'),'17.5339','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('76',convert(money,'8.18'),'17.3633','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('77',convert(money,'7.92'),'16.4754','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('78',convert(money,'6.36'),'16.374','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('79',convert(money,'9.20'),'16.2018','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('80',convert(money,'10.09'),'16.2013','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('81',convert(money,'8.78'),'15.7496','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('82',convert(money,'4.95'),'15.6086','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('83',convert(money,'8.20'),'15.4618','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('84',convert(money,'7.63'),'15.3775','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('85',convert(money,'7.06'),'15.2405','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('86',convert(money,'8.18'),'15.2229','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('87',convert(money,'6.88'),'15.1594','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('88',convert(money,'7.46'),'15.0574','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('89',convert(money,'9.97'),'14.4833','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('90',convert(money,'8.45'),'14.3658','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('91',convert(money,'5.54'),'14.353','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('92',convert(money,'4.72'),'14.2415','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('93',convert(money,'10.08'),'14.0523','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('94',convert(money,'7.65'),'13.8778','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('95',convert(money,'7.35'),'13.7063','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('96',convert(money,'5.19'),'13.3039','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('97',convert(money,'7.29'),'13.1952','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('98',convert(money,'7.64'),'13.188','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('99',convert(money,'7.74'),'13.0517','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('100',convert(money,'2.62'),'12.9761','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('101',convert(money,'4.35'),'12.834','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('102',convert(money,'6.46'),'12.5904','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('103',convert(money,'9.53'),'12.5893','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('104',convert(money,'5.91'),'12.4486','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('105',convert(money,'6.80'),'12.2639','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('106',convert(money,'6.69'),'12.2329','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('107',convert(money,'6.37'),'12.2204','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('108',convert(money,'7.36'),'11.9331','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('109',convert(money,'7.63'),'11.5979','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('110',convert(money,'5.67'),'11.57','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('111',convert(money,'6.52'),'11.5695','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('112',convert(money,'6.74'),'11.5054','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('113',convert(money,'6.37'),'10.979','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('114',convert(money,'6.24'),'10.9037','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('115',convert(money,'9.18'),'10.8605','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('116',convert(money,'6.54'),'10.8433','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('117',convert(money,'6.21'),'10.6319','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('118',convert(money,'6.78'),'10.5205','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('119',convert(money,'5.35'),'10.1602','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('120',convert(money,'7.21'),'10.135','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('121',convert(money,'5.03'),'9.96296','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('122',convert(money,'6.48'),'9.95423','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('123',convert(money,'7.31'),'9.94387','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('124',convert(money,'5.03'),'9.71744','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('125',convert(money,'6.30'),'9.63011','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('126',convert(money,'6.06'),'9.60822','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('127',convert(money,'4.96'),'9.54318','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('128',convert(money,'3.65'),'9.36709','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('129',convert(money,'6.38'),'9.26422','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('130',convert(money,'4.13'),'9.11232','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('131',convert(money,'4.79'),'9.08303','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('132',convert(money,'7.17'),'8.94436','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('133',convert(money,'6.48'),'8.89934','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('134',convert(money,'5.65'),'8.87636','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('135',convert(money,'4.27'),'8.87305','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('136',convert(money,'7.83'),'8.73056','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('137',convert(money,'6.13'),'7.96018','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('138',convert(money,'6.28'),'7.911','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('139',convert(money,'4.13'),'7.61774','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('140',convert(money,'5.94'),'7.39469','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('141',convert(money,'4.22'),'6.85944','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('142',convert(money,'3.34'),'6.81982','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('143',convert(money,'6.60'),'6.56834','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('144',convert(money,'5.77'),'6.4892','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('145',convert(money,'3.08'),'5.64715','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('146',convert(money,'4.38'),'5.36118','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('147',convert(money,'3.39'),'5.28177','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('148',convert(money,'6.22'),'5.18103','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('149',convert(money,'5.10'),'5.15438','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('150',convert(money,'6.68'),'5.05164','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('151',convert(money,'5.72'),'5.0001','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('152',convert(money,'8.56'),'4.33456','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('153',convert(money,'5.03'),'4.01306','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('154',convert(money,'5.59'),'3.41515','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('155',convert(money,'0.00'),'3.30027','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('182',convert(money,'12.78'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('181',convert(money,'8.39'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('180',convert(money,'15.53'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('179',convert(money,'10.40'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('178',convert(money,'16.09'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('177',convert(money,'7.49'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('176',convert(money,'3.50'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('175',convert(money,'6.70'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('174',convert(money,'8.26'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('173',convert(money,'0.00'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('172',convert(money,'0.00'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('171',convert(money,'9.07'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('170',convert(money,'13.61'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('161',convert(money,'9.17'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('168',convert(money,'7.23'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('167',convert(money,'0.00'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('166',convert(money,'6.11'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('165',convert(money,'7.86'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('164',convert(money,'0.00'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('163',convert(money,'7.52'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('162',convert(money,'8.75'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('183',convert(money,'5.05'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('160',convert(money,'0.00'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('159',convert(money,'0.00'),'0','C')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('158',convert(money,'10.27'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('157',convert(money,'6.85'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('156',convert(money,'0.00'),'0','B')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('169',convert(money,'8.08'),'0','A')
INSERT OptimalCombo(ID,Price,Value,Part) VALUES('184',convert(money,'4.45'),'0','B')
DML and DDL for the Raw table above.

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