Reference no: EM132477502

MGSC405 - Quantitative Approaches to Decision Making - Athabasca University

Question 1

The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost?

	Type A	Type B
Shade tolerance	1	1
Traffic resistance	2	1
Drought resistance	2	5

Question 2

Use the following Management Scientist output to answer the questions.

LINEAR PROGRAMMING Question

MAX 31X1+35X2+32X3

S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120

OPTIMAL SOLUTION

Objective Function Value = 763.333

Variable	Value	Reduced Cost
X1	13.333	0.000
X2	10.000	0.000
X3	0.000	10.889

 

Constraint	Slack/Surplus	Dual Price
1	0.000	-0.778
2	0.000	5.556
3	23.333	0.000

OBJECTIVE COEFFICIENT RANGES

Variable	Lower Limit	Current Value	Upper Limit
X1	30.000	31.000	No Upper Limit
X2	No Lower Limit	35.000	36.167
X3	No Lower Limit	32.000	42.889

RIGHT HAND SIDE RANGES

Constraint	Lower Limit	Current Value	Upper Limit
1	77.647	90.000	107.143
2	126.000	150.000	163.125
3	96.667	120.000	No Upper Limit

a. Give the solution to the Question.
b. Which constraints are binding?
c. What would happen if the coefficient of x1 increased by 3?
d. What would happen if the right-hand side of constraint 1 increased by 10?

Question 3
National Wing Company (NWC) is gearing up for the new B-48 contract. Currently NWC has 100 equally qualified workers. Over the next three months NWC has made the following commitments for wing production:

Month	Wing Production
May	20
June	24
July	30

?Each worker can either be placed in production or can train new recruits. A new recruit can be trained to be an apprentice in one month. The next month, he, himself, becomes a qualified worker (after two months from the start of training). Each trainer can train two recruits. The production rate and salary per employee is estimated below.

Employee	Production Rate (Wings/Month)	Salary Per Month
Production	.6	$3,000
Trainer	.3	3,300
Apprentice	.4	2,600
Recruit	.05	2,200

?At the end of July, NWC wishes to have no recruits or apprentices but have at least 140 full-time workers. Formulate and solve a linear program for NWC to accomplish this at minimum total cost.

Question 4

A plant manager for a sporting goods manufacturer is in charge of assigning the manufacture of four new aluminum products to four different departments. Because of varying expertise and workloads, the different departments can produce the new products at various rates. If only one product is to be produced by each department, and the daily output rates are given in the table below, which department should manufacture which product to maximize total daily product output? (Note: Department 1 does not have the facilities to produce golf clubs.)

? Department	Baseball Bats	Tennis Rackets	Golf Clubs	Racquetball Rackets
1	100	60	X	80
2	100	80	140	100
3	110	75	150	120
4	85	50	100	75

?
?Formulate this assignment Question as a linear program.

Question 5

Peaches are to be transported from three orchard regions to two canneries. Intermediate stops at a consolidation station are possible.

Orchard	Supply	Station	Cannery	Capacity
Riverside	1200	Waterford	Sanderson	2500
Sunny Slope	1500	Northside	Millville	3000
Old Farm	2000

Shipment costs are shown in the table below. Where no cost is given, shipments are not possible. Where costs are shown, shipments are possible in either direction.

	R	SS	OF	W	N	S	M
Riverside		1		5		3
Sunny Side				4	5
Old Farm				6	3
Waterford					2	2	4
Northside						5	9
Sanderson							2
Millville

Draw the network model for this Question.

Attachment:- Quantitative Approaches to Decision Making.rar