Respuesta :
a. If he uses the maximin criterion, the small bus will be purchase.
b. If he uses the minimax regret criterion, the medium or the larger will be purchase.
c. The small bus will be purchase.
Under the maximin criterion:
Under the criterion, the manager will want to maximize the minimum possible profit (pessimistic criterion) , thus, the profits will be:
Bus Size Demand
Low Medium High
Small 50 60 70 → min profit = 50
Medium 40 80 90 → min profit = 40
Large 20 50 120 → min profit = 20
Therefore, the option with maximum minimum profit is the small size.
Under the maximin criterion:
Manager will want to minimise the maximum possible loss , thus the losses respect with the best profit option will be:
Bus Size Demand
Low Medium High
Small 0 -20 -50 → max loss= -50
Medium -10 0 -30 → max loss = -30
Large -30 -30 0 → max loss = -30
Therefore, the option with minimum maximum loss is the medium or the large one.
Expected value of each option:
Small bus:
= 30/100*50 +30/100*60 +40/100*70
= 61
Medium bus:
= 30/100*40 +30/100*80 +40/100*90
= 72
Large bus:
= 30/100*20 +30/100*50 +40/100*120
= 69
Therefore, the small bus option is the better one, since it has the maximum expected profit
Full question "The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows: (a) If he uses the maximin criterion, which size bus will he decide to purchase? (b) If he uses the minimax regret criterion, which size bus will he decide to purchase? (c) If he feels the chances of low, moderate, and high demand are 30%, 30%, and 40% respectively, which size bus will he decide to purchase and what is the expected annual profit for this option?
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