Obtain the initial solution for the following problem

Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

Here O_i and D_j represent i^th origin and j^th destination.

Obtain an initial basic feasible solution to the following transportation problem using least cost method.

Here O_i and D_j denote i^th origin and j^th destination respectively.

Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

Cost are expressed in terms of rupees per unit shipped.

Solve the following assignment problem.

Consider the following pay-off (profit) matrix Action States

Action	States
	(s1)	(s2)	(s3)	(s4)
A1	5	10	18	25
A2	8	7	8	23
A3	21	18	12	21
A4	30	22	19	15

Determine best action using maximin principle.

A business man has three alternatives open to him each of which can be followed by any of the four possible events. The conditional pay offs for each action - event combination are given below:

Alternative	Pay – offs (Conditional events)
	A	B	C	D
X	8	0	-10	6
Y	-4	12	18	-2
A3	14	6	0	8

Determine which alternative should the businessman choose, if he adopts the maximin principle.

Consider the following pay-off matrix

Alternative	Pay – offs (Conditional events)
	A1	A2	A3	A4
E1	7	12	20	27
E2	10	9	10	25
E3	23	20	14	23
E4	32	24	21	17

Using minmax principle, determine the best alternative.

Find an initial basic feasible solution of the following problem using north west corner rule.

Determine an initial basic feasible solution of the following transportation problem by north west corner method

Obtain an initial basic feasible solution to the following transportation problem by using least- cost method.

Determine basic feasible solution to the following transportation problem using North west Corner rule.

Find the initial basic feasible solution of the following transportation problem :

Using (i) North West Corner rule
(ii) Least Cost method
(iii) Vogel’s approximation method

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below.
Determine the allocation that minimizes the overall processing cost.

(cost is in Rs. per unit)

Given the following pay-off matrix(in rupees) for three strategies and two states of nature.

Strategy	States-of-nature
	E1	E2
S1	40	60
S2	10	-20
S3	-40	150

Select a strategy using each of the following rule
(i) Maximin
(ii) Minimax

A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.

Rainfall	Estimated Conditional Profit(Rs.)
	crop A	crop B	crop C
High	8000	3500	5000
Medium	4500	4500	5000
Low	2000	5000	4000

If the farmer wishes to plant only crop, decide which should be his best crop using
(i) Maximin
(ii) Minimax

The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

Types of shampoo	Estimated Sales (in Units)
	15000	10000	5000
Egg shampoo	30	10	10
Clinic Shampoo	40	15	5
Deluxe Shampoo	55	20	3

What will be the marketing manager’s decision if
(i) Maximin and
(ii) Minimax principle applied?

Following pay-off matrix, which is the optimal decision under each of the following rule
(i) maxmin
(ii) minimax

Act	States of nature
	S1	S2	S3	S4
A1	14	9	10	5
A2	11	10	8	7
A3	9	10	10	11
A4	8	10	11	13

The following table summarizes the supply, demand and cost information for four factors S₁, S₂, S₃, S₄. shipping goods to three warehouses D₁, D₂, D₃.

Find an initial solution by using north west corner rule. What is the total cost for this solution?

A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:

Alternative	Economic conditions
	High growth(Rs.)	Normal growth(Rs.)	Slow growth (Rs.)s
Stocks	10000	7000	3000
Bonds	8000	6000	1000
Debentures	6000	6000	6000

Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax.