Reference no: EM133335287

Quantitative Analysis for Management Decisions

Question 1: A manufacturing firm has discontinued production of a certain unprofitable product line. This created considerable excess production capacity. Management is considering to devote this excess capacity to one or more of three product 1,2 and 3. The available capacity on the machines which might limit output are given below:

Machine type Available time (in machine hours per week)

Milling machine   250

Lathe                     150

Grinder                 50

The number of machine hours required for each units of the respective product is given below;

Machine type	Productivity (in machine hours/unit)
	Product 1	Product 2	Product 3
Milling	8	2	3
Lathe	4	3	0
Grinder	2	0	1

The unit profit would be 20 birr, 6 birr and 8 birr for products 1,2 and 3. Find how much of each product the firm should produce in order to maximise profit ? Solve the problem by simplex method.

Question 2. Write the dual of following problems:

(a) Maximize Z = 7X₁ + 5X₂

Subject to:

X₁ + 2X₂ ≤ 6

4X₁ + 3X₂ ≤ 12

X₁, X₂ ≥ 0

(b) Maximize Z= 3X₁ + 4X₂

Subject to:
5X₁ + 4X₂ ≤ 200
3X₁ + 5X₂ ≤ 150
8X₁ + 4X₂ ≥ 80

X₁, X₂ ≥ 0

Question 3. Obtain an initial basic feasible solution to the following transportation problem using Vogel's approximation method.

	D1	D2	D3	D4
A	5	1	3	3	34
B	3	3	5	4	15
C	6	4	4	3	12
D	4	-1	4	2	19
	21	25	17	17	80

Question 4. Four jobs are to be done on four different machines. The cost in rupees of producing ith on the jth machine is given below. Assign the jobs to different machines so as to minimise the total cost.

Jobs	M1	M2	M3	M4
J1	15	11	13	15
J2	17	12	12	13

Question 5. In a small town, there are two discount stores ABC and XYZ. They are the only stores that handle the festival goods. The total number of customers is equally divided between the two because the price and quality of goods sold are equal. Both stores have good reputations in the community, and they render equally good customer services. Assume that a gain of customer by ABC is a loss to XYZ and vice versa.

Both stores plan to run annual pre-Christmas sale during the first week of December. Sales are advertised through the local newspaper, radio and television media. With the aid of advertising the payoff for ABC store is constructed and given below.

                                                                                           XYZ store

	News paper	radio	Television
News paper	30	40	-80
ABC   radio	0	15	-20
Television	90	20	50

Find optimal strategies for both stores and the value of the game.