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P1

The Livewright Medical Supplies Company
	Variables	s: # of salespeople assigned to the south				e: # of salespeople assigned to the east
		m: # of salespeople assigned to the midwest
	maximize			profit
	subject to	s+e+m <= 12		total number of salespeople constraint
		s <= 5		max number of salespeople assigned to the south
				expense constraint
		s,e,m are integers		integer constraints
			Profit	Total Sales	Sales South	Expense
	s			1	1
	e			1	0
	m			1	0
			Usage
				<=	<=
			Availabe	12	5
	Profit

P2

Solve the mixed integer linear programming model
	maximize	5x1 + 6x2 + 4x3
	Subject to	5x1 + 3 x2 + 6x3 <= 20
		x1 + 3x2 <= 12
		x1, x3 => 0
		x2 => 0 and integer
			Obj. Coefficients	Constraint 1	Constraint 2
	x1
	x2
	x3
			Usage
			Available
	Objective

P3

Texas Consolidated Electronics Company
		Project	Estimated Profit (1000000s)	Expense ($1,000s)	Management Scientists required	Project Selection constraints
			(1,000,000s)
		1	0.36	60	7
		2	0.82	110	9
		3	0.29	53	8
		4	0.16	47	4
		5	0.56	92	7
		6	0.61	85	6
		7	0.48	73	8
		8	0.41	65	5
	Constraints		Usage
				<=	<=	>=
			Available	300	40
	DV	Project
		1
		2			Please include the following constraints in your solutions
		3
		4			Note: selection constraint p5 >= p2
		5			- p2 + p5 >= 0
		6			Note: All projects variables must be binary
		7
		8
	Objective	Maximize Profits

P4

Terraco Motor Company
		From Plant	Transportation Costs ($1000s)				Annual Production Capacity	Annual Fixed Operating Costs
			to Warehouse
			A	B	C	D
		1	56	21	32	65	12,000	2,100,000
		2	18	46	70	35	18,000	850,000		Note F7 cell should be $70 NOT $7
		3	12	71	41	52	14,000	1,800,000
		4	30	24	61	28	10,000	1,100,000
		5	45	50	26	31	16,000	900,000
		Annual	6,000	14,000	8,000	10,000
		Demand
	DV	Plant to warehouse	A	B	C	D	Shipped		Plant Capacity
		1					0	<=	0
		2						<=	0
		3						<=	0
		4						<=	0
		5						<=	0
			0
			=	=	=	=
		Annual Demand	6,000	14,000	8,000	10,000
	DV	Plants Operation
		1			Variables:	xij: vehicles shipped from plant i to warehouse j where i = 1,2,3,4,5 and j = A,B,C,D
		2				pi: = 0 plant i will be closed down; = 1 plant i will be open where i = 1,2,3,4,5
		3
		4			minimize	Total shipping cost + Total operating cost
		5			subject to	Total shipment from plant i <= pi*plant i capacity where i= 1,2,3,4,5
						Total received by warehouse j = demand of warehouse j where j=A,B,C,D
	Objective	Minimize Cost	$0

1

2

3

4

5

6

7

8

A

B

C

D

Terraco Motor Company

A

1

56

2

18

3

12

From Plant

Transportation Costs ($1000s)

to Warehouse