Question

Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming month. Orders for the bicycles must be placed in quantities of twenty (20). If Zed and Adrian run out of bicycles during the month, then they will suffer a loss of "goodwill" among their customers. Zed and Adrian estimate that the demand for bicycles this month will be 10, 30, 50, or 70 bicycles but the probabilities for these possibilities are unknown. The table below depicts profit that results from each possibility. Strategy Order 20 Order 40 Order 60 Order 80 State of Nature Demand 10 Demand 30 Demand 50 Demand 70 $50 $550 $450 -$330 $770 $1270 $1170 $650 $450 $1550 $2050 $970 $130 $1230 $2330 Part A: Determine the best strategy using the maxi-min criterion. Show work that supports your answer. Part B: Determine the best strategy using the maxi-max criterion. Show work that supports your answer.

Answer 1

Criterion table Criterion Expected Value Maximax Maximin Minimax Action Buy 20 Buy 40 Buy 60 Buy 80 Best Action 400 740 720 460 Buy 40 1270 2050 2330 Buy 80 50 -330 -650 -970 Buy 20 1980 1160 7 00 1020 Buy 60 550

a)

Maximax Criterion

The maximax criterion is far easier to try and do than the arithmetic mean. you merely study the most effective you'll do underneath every

action (the largest variety in each column) You then take the most effective (largest) of those.

The largest payoff if you get twenty, 40, 60, and eighty bicycles are $550, 1270, 2050, and 2330 severally. Since the most important of these is $2330, you'd get eighty bicycles

B)

Maximin Criterion

The maximin criterion is as simple to try and do because the maximax Except rather than taking the most important vanity underneath

every action, you are taking the tiniest payoff underneath every action (smallest vanity in each column) You then take the most effective(largest of these)

The smallest payoff if you get twenty, 40, 60, and eighty bicycles are $50, 330, 650, and -970 severally Since the most important of these is $50, you'd get twenty bicycles

C)

Minimax Criterion

Be sure to use the timeserving loss (regret) table for the minimax criterion. you are taking the most important loss underneath every action

(largest vanety in each column). You then take the tiniest of those (it is loss, afterall)

The largest losses if you get twenty, 40, 60, and eighty bicycles are $1980, 1160, 700, and 1020 severally. Since the tiniest of these is $700,you'd get sixty bicycles