Reference no: EM132270012

Homework Problems -

Part A -

1. An airline is preparing to replace its old planes with three new styles of jets. The airline needs 17 new planes to service its current routes. The decision regarding which planes to purchase should balance cost with capability factors, including the following:

(1) The airline can finance up to $700 million in purchases;

(2) Each 7A7 jet will cost $38 million, each 7B7 jet will cost $27 million, and each 7C7 jet will cost $22 million;

(3) At least one-third of the pins purchased should be the longer-range 7A7;

(4) The annual maintenance budget it to be no more than $12 million;

(5) The annual maintenance cost pa 7A7 is estimated to be $800,000, $600,000 for each 7B7, and $500,000 for each 7C7; and

(6) Annually, each 7A7 can carry 125,000 passengers, each 7B7 can fly 95,000 passengers, and each 7C7 can fly 80,000 passengers.

Formulate this as an IP problem to maximize the annual passenger-carrying capability. Solve it by using Excel.

2. A hospital is planning an S8 million addition to its existing facility. The architect has been asked to consider the following design parameters:

(1) There should be at least 10 and no more than 20 intensive care unit (ICU) rooms;

(2) There should be at least 10 and no more than 20 cardiac care unit (CCU) rooms;

(3) There should be no more than 50 double rooms;

(4) There should be at least 35 single rooms; and

(5) All patient rooms should fit inside the allotted 40,000-square-foot space (not including hallways).

The following table summarizes the relevant room data:

	SINGLE	DOUBLE	ICU	CCU
Cost per room to build and furnish ($ thousands)	$45	$54	$110	$104
Minimum square feet required	300	360	320	340
Profit per room per month ($ thousands)	$21	$28	$48	$41

How many rooms of each type should the architect include in the new hospital design?

3. Stockbroker Susan Drexler has advised her client at shown in the following table:

INVESTMENT	COST (THOUSANDS)	EXPECTED RETURN (THOUSANDS)
Andover municipal bonds	$400	$35
Hamilton city bonds	$1,000	$100
East Power & Light Co.	$350	$30
Nebraska Electric Service	$700	$65
Southern Gas and Electric	$490	$45
Manuel Products Co.	$270	$20
Builders Paint Co.	$800	$90
Rest Easy Hostels Co.	$500	$50

The client agrees to this list but provides several conditions:

(1) No more than $3,000,000 be invested.

(2) The money is to be spread among at least five investments.

(3) No more than one type of bond can be purchased.

(4) At least two utility stocks must be purchased, and

(5) At least two regular stocks must be purchased.

Formulate this as a 0-1 IP problem for Ms. Drexler to maximize expected return. Solve it by using Excel.

Part B -

1. A certification program consists of series of activities that must be accomplished in a certain order. The activities, their immediate predecessors, and estimated durations appear in the following table.

ACTIVITY	IMMEDIATE PREDECESSORS	TIME (DAYS)
A	-	2
B	-	5
C	-	1
D	B	10
E	A, D	3
F	C	6
G	E, F	8

(a) Develop the project network for the certification program.

(b) Determine the EST, EFT, LST, LFT and slack for each activity. Also determine the total program completion time and the critical path(s).

2. The Pickett Marketing Firm is developing a new Web-based media campaign for a client. The following table describes the relationships between the activities that need to be completed.

ACTIVITY	IMMEDIATE PREDECESSORS	TIME (DAYS)
A	-	4
B	A	6
C	B	12
D	B	11
E	D	9
F	D	8
G	D	10
H	C	5
I	C	7
J	E, F, G	4
K	H, I	9

(a) Develop the project network for this problem.

(b) Determine the EST, EFT, LST, LFT and slack for each activity. Also determine the total project completion time and the critical path(s).

3. An office complex is to be renovated. Before the job can be completed, various trades people and skilled workers must install their materials. The table describes the relationships between the activities that need to be completed.

ACTIVITY	IMMEDIATE PREDECESSORS	TIME (DAYS)
A1		5
A2	A1	6
A3	A1	2
A4	A1	9
A5	A2	9
A6	A3, A4	3
A7	A4	7
A8	A4	4
A9	A5, A6, A7	6
A10	A8	5

(a) Develop a project network for this problem.

(b) Determine the EST, EFT, LST, LFT and slack for each activity. Also determine the total project completion time and the critical path(s).