Question

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Green Ltd Question Green Ltd specialises in the manufacture of naturally enriched soil for use in the horticulture industry. Demand varies with weather conditions. Management are trying to work out the level of production required for the coming year in order to maximise profits. The company doesn't want to miss out on the opportunity periods of good weather present; however, it also does not want to be left with large quantities of unsold product at the end of the year, as the space required for storage has multiple alternative uses. Green Ltd has received the following estimates about the probable weather conditions and corresponding demand levels for the coming year: Weather Probability Demand Good 25% 3,500 bags Average 2,800 bags Bad 30% 2,000 bags Da 45% Each bag sells for €90 and costs €40 to make. Any product unsold at the end of the year has to be disposed of at a cost of €5 per bag. Green Ltd has decided to produce at one of the three levels of production to match forecast demand. The company has asked for your help in deciding which level of production to select. Required: (A) Distinguish between risk and uncertainty. (B) Decide the level of production (number of bags) based on each of the following decision rules: (i) Maximin; (ii) Maximax. Construct a pay-off table as part of your answer. Explain the rationale underpinning your decision in each instance.

Answer 1

	Risk arises where certain information is not available
	Risk is mesurable with available information through probabilities
	Uncertainty arises when information is not available
	Uncertainty cannot be measured
	Risk can be measured and managed
	Uncertainty can neither be measured, nor managed
	PAY OFF MATRIX
				PAYOFF AT PRODUCTION LEVELS
	Weather	Demand	Probability	3500	2800	2000
	Good	3500	0.25	€         175,000	€      140,000	€       100,000
	Average	2800	0.45	€         108,500	€      140,000	€       100,000
	Bad	2000	0.3	€           32,500	€        64,000	€       100,000
	Profit from sales of one Bag=90-40=	€              50.00
	Payoff on each unsold bag =40+5=	€           (45.00)
	Payoff for Demand 3500 and Production 3500	€         175,000	(3500*50)
	Payoff for Demand 2800 and Production 2800	€         140,000	(2800*50)
	Payoff for Demand 2000 and Production 2000	€         100,000	(2000*50)
	Payoff for Demand 3500 and Production 2800	€         140,000	(2800*50)
	Payoff for Demand 3500 and Production 2000	€         100,000
	Payoff for Demand 2800 and Production 3500	€         108,500	(2800*50-(3500-2800)*45)
	Payoff for Demand 2800 and Production 2000	€         100,000
	Payoff for Demand 2000 and Production 2800	€           64,000	(2000*50-(2800-2000)*45
	Payoff for Demand 2000 and Production 3500	€           32,500	(2000*50-(3500-2000)*45
(i)	Maximin rule selects the alternative which maximizes minimum payoff available
	In this case the decision maker is minimizing his losses and not willing to take risk
	Minimum payoff for production level of 3500	€           32,500
	Minimum payoff for production level of 2800	€           64,000
	Minimum payoff for production level of 2000	€         100,000
	LEVEL OF PRODUCTION UNDER MAXIMIN RULE	2,000	Bags
(ii)	Maximax rule selects the alternative which maximizes maximum payoff available
	In this case the decision maker is willing to take maximum risk
	Maximum payoff for production level of 3500	€         175,000
	Maximum payoff for production level of 2800	€         140,000
	Maximum payoff for production level of 2000	€         100,000
	LEVEL OF PRODUCTION UNDER MAXIMAX RULE	3,500	Bags