Question

Cambridge Ltd is currently suffering from a depression in the market for its products and needs to decide which of three products it should continue produce, so that it can maximise its profits. They have recently employed the services of Research It Ltd who have researched Cambridge Ltd and their products and have produced the following information:

Research It Ltd. have provided information for three levels of demand, low, medium and high and a probabilities for each level of demand as 10%, 50% and 40% respectively.

The net incomes for each product are:
Product A: £50,000, £110,000, £145,000
Product B: £120,000, £175,000, £220,000
Product C: £180,000, £200,000, £230,000

Required:
a. Construct the payoff table for the three products.
b. Produce, where needed, information which will allow you to state which product you would recommend that management produce, if using the following decision rules:
(i) The maximin rule
(ii) The maximax rule
(iii) The minimax regret rule
(iv) Expected value of profit
c. Desk and Field research have been discussed, especially which approach would benefit Cambridge Ltd the most. Briefly explain the 2 types of research.

I would really appreciate if you explain widely part c of the question.

Answer 1

Part a.

Pay off the table

	LOW	MEDIUM	HIGH
Product A	50000	110000	145000
Product B	120000	175000	220000
Product C	180000	200000	230000
Probability	0.1	0.5	0.4

Part b.

i = The maximin rule=

	LOW	MEDIUM	HIGH	Min
Product A	50000	110000	145000	50000
Product B	120000	175000	220000	120000
Product C	180000	200000	230000	180000

We will select the maximum value from the min column so the best decision will be Product C

ii= maximax rule=

	LOW	MEDIUM	HIGH	Max
Product A	50000	110000	145000	145000
Product B	120000	175000	220000	220000
Product C	180000	200000	230000	230000

We will select the maximum value from the max column so the best decision will be Product C

iii= minimax regret rule=

For regret table=

	LOW	MEDIUM	HIGH
Product A	180000-50000	200000-110000	230000-145000
Product B	180000-120000	200000-175000	230000-220000
Product C	180000-180000	200000-200000	230000-230000

Regret table=

	LOW	MEDIUM	HIGH
Product A	130000	90000	85000
Product B	60000	25000	10000
Product C	0	0	0

	LOW	MEDIUM	HIGH	Max
Product A	130000	90000	85000	130000
Product B	60000	25000	10000	60000
Product C	0	0	0	0

We will select the minimum value from the max column so the best decision will be Product C

iv= Expected value of profit rule=

EVP for Product A=50000*0.1+110000*0.5+145000*0.4 =118000

EVP for Product B=120000*0.1+175000*0.5+22000*0.4=108300

EVP for Product C==180000*0.1+200000*0.5+23000*0.4=127200

We will select the minimum value from the EVP so the best decision will be Product C

Part c.

They can use either exploratory research in which they can try to find out the best-suited method or option for the company or they can also go for the descriptive research in which they can describe the details of the different options that can be taken by the company and depending upon that a decision can be taken.