week 8 Homework problem>>>>>xoon only

P14

Grafton Metalworks Company
		Ore	Metal (%)				Impurities	Cost/Ton
			A	B	C	D
		1	0.19	0.15	0.12	0.14	0.4	27
		2	0.43	0.1	0.25	0.07	0.15	25
		3	0.17	0	0	0.53	0.3	32
		4	0.2	0.12	0	0.18	0.5	22
		5	0	0.24	0.1	0.31	0.35	20
		6	0.12	0.18	0.16	0.25	0.29	24
	Composition constraints			A		>=	0.21
				B		<=	0.12
				C		<=	0.07
				D		>=	0.3
				D		<=	0.65
	Impurity constraint			Metal		=	1
			Ore
	Decision variables
			1
			2
			3
			4
			5
			6
	Objective function		Minimize Cost ($)

P19

congressman’s district
		Program	Votes/ Dollar
		Job training	0.02
		Parks	0.09
		Sanitation	0.06
		Mobile library	0.04
	Constraints	Job training	<=	1600000
		Parks	<=	1600000
		Sanitation	<=	1600000
		Mobile library	<=	1600000
		Parks	<=
		Job training	>=
	spending		=	4000000
	Decision Variables		Job training
			Parks
			Sanitation
			Mobile library
	Objective	Maximize Votes

P20

Anna Broderick Lunch Menu
				Calories	Iron	Protein	Carbo-hydrates	Fat (g/lb.)	Chol-esterol	Cost
				(per lb.)	(mg/lb.)	(g/lb.)	(g/lb.)		(mg/lb.)
										$/lb.
			Chicken	520	4.4	17	0	30	180	0.8
			Fish	500	3.3	85	0	5	90	3.7
			Ground beef	860	0.3	82	0	75	350	2.3
			Dried beans	600	3.4	10	30	3	0	0.9
			Lettuce	50	0.5	6	0	0	0	0.75
			Potatoes	460	2.2	10	70	0	0	0.4
			Milk (2%)	240	0.2	16	22	10	20	0.83
	Constraints			>=	>=	>=	>=	>=	<=
				1500	5	30	40	20	30
				<=				<=
				2000				60
	Decision Variables		Chicken		<=	0.5
			Fish		<=	0.5
			Ground beef		<=	0.5
			Dried beans		<=	0.5
			Lettuce		<=	0.5
			Potatoes		<=	0.5
			Milk (2%)
	Objective		Minimize Cost ($)
	a.      If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution?
			Answer:

P22

Cabin Creek Coal (CCC)
			Plant
		Mine	1	2	3	4	Constraints		Mine Capacity (tons)
		1	$69	$71	$72	$74		<=	220
		2	66	74	75	79		<=	170
		3	86	89	80	82		<=	280
		Constraints
			=	=	=	=
		Demand (tons)	110	160	90	180
			Mine	% Ash	% Sulfur			Plant	1	2	3	4
			1	0.09	0.06		Constraints
			2	0.05	0.04				<=		<=
			3	0.04	0.03		Ash		6		5
							Constraints
									<=		<=
							Sulfur		5		7
		Mine to Plant					Constraints
	DV	x11								<=		<=
		x12					Ash + Sulfur			5		6
		x13
		x14
		x21
		x22
		x23
		x24
		x31
		x32
		x33
		x34
	Objective function		Minimize Cost

P36

Joe Henderson Assignments
1, 2		Operator	Drill Press (min)	Lathe (min)	Grinder (min)
		1	22	18	35
		2	41	30	28
		3	25	36	18
	DV	Operator	Drill Press	Lathe	Grinder	Operator Constraints		Assignment
		1					=	1
		2					=	1
		3					=	1
		Machine Constraints
			=	=	=			Note: Constraints		=	Integer
			1	1	1
	Objective	Minimize Time
3		Operator	Drill Press (min)	Lathe (min)	Grinder (min)
		1	22	18	35
		2	41	30	28
		3	25	36	18
		4	20	20	20
	DV	Operator	Drill Press	Lathe	Grinder	Operator Constraints		Assignment
		1	0	1	0		<=	1
		2	0	0	0		<=	1
		3	0	0	1		<=	1
		4	1	0	0		<=	1
		Machine Constraints
			=	=	=			Note: Constraints		=	Integer
			1	1	1
	Objective	Minimize Time
	Answer	Should Joe hire Fred's wihe?				(Yes / No)

P43

Cash and Carry Building Supply Company
		Length	Order (quantity)
		7 ft.	700
		9 ft.	1,200
		10 ft.	300
	What are possible patterns the standard board can be cut?
			Possible cut patterns
			#1	#2	#3	#4	#5	#6	Constraints		Order (quantity)
		7	3	2	2	1	0	0		=	700
		9	0	0	1	2	1	0		=	1,200
		10	0	1	0	0	1	2		=	300
		Total length	21	24	23	25	19	20
			<=	<=	<=	<=	<=	<=
			25	25	25	25	25	25
	Decision Variables
	Objective	Minimize standard boards
	What are possible patterns the standard board can be cut?
			Possible cut patterns
			#1	#2	#3	#4	#5	#6	Constraints		Order (quantity)
		7	3	2	2	1	0	0		>=	700
		9	0	0	1	2	1	0		>=	1,200
		10	0	1	0	0	1	2		>=	300
		Total length	21	24	23	25	19	20
		Trim Loss	4	1	2	0	6	5
	Decision Variables
	Objective	Minimize standard boards

1

2

3

4

5

6

7

A

B

C

Cash and Carry Building Supply Company

Length

7 ft.

9 ft.

10 ft.