Question

can you do a-e please, thank you for your effort!

O B IC CLICUIUI! 2. Aggie Theme Park Inc. must place an order for ponchos to sell to customers during rain + showers. Ponchos are sold for $1. The demand for ponchos depends on the level of rain in the summer. Rain for the summer may be light, normal, heavy or very heavy with probabilities of 0.20, 0.40., 0.25, and 0.15 respectively. Ponchos are purchased by the pallet. One pallet of 10,000 ponchos costs $5,000. Ponchos not sold at the end of the summer can be returned at a value of $0.20 each. Past experience shows that demand for a dry season is 13,000, a normal season is 19,000, a wet season is 28,000 and a very wet season is 36,000. a. Construct the payoff table for this problem. Justify your list of actions. b. What decision should be made according to the maximax decision rule? c. What decision should be made according to the maximin decision rule? d. What decision should be made according to the minimax regret decision rule? e. What decision should be made according to the expected value decision rule? OC T unglior .. .

Answer 1

In the given question,

Sales Price of ponchos = $1

Cost Price of ponchos = $5000/ $10,000 = $0.5

Profit from each ponchos sold = $1 - $0.5 = $0.5

Ponchos can be ordered by pallet and one pallet contains 10,000 ponchos

If unsold, ponchos can be returned at $0.2

Loss from each ponchos unsold = $0.5 - $0.2 = $0.3

a. Payoff table would be as follows

			Supply
Season	Demand	Probability	10,000 units	20,000 units	30,000 units	40,000 units
Dry Season	13,000	0.20	$5000 (10000 * $0.5)	$4400 (13000* $0.5 -7000 * $0.3)	$1400 (13000* $0.5 - 17000 * $0.3)	($1600) (13000* $0.5 - 27000 * $0.3)
Normal Season	19,000	0.40	$5000 (10000 * $0.5)	$9200 (19000* $0.5 -1000 * $0.3)	$6200 (19000* $0.5 - 11000 * $0.3)	$3200 (19000* $0.5 - 21000 * $0.3)
Wet Season	28,000	0.25	$5000 (10000 * $0.5)	$10000 (20000 * $0.5)	$13400 (28000* $0.5 - 2000 * $0.3)	$10,400 (28000* $0.5 - 12000* $0.3)
Very Wet Season	36,000	0.15	$5000 (10000 * $0.5)	$10000 (20000 * $0.5)	$15000 (30000 * $0.5)	$16800 (36000* $0.5 - 4000* $0.3)

b. MAXIMAX

The maximax rule involves selecting the alternative that maximises the maximum payoff available.

Looking at the payoff table, the highest maximum possible pay-off is $16800. This happens if we order for 40,000 ponchos and the season turns out to be Very wet season with a demand of 36000 units.

Aggie Theme park Inc. should therefore decide to place an order of 40,000 ponchos under the maximax rule

c. MAXIMIN

The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. The investor would look at the worst possible outcome at each supply level, then selects the highest one of these.

Looking at the payoff table

• If we order 10,000 units, the minimum payoff would be $5000
• If we order 20,000 units, the minimum payoff would be $4400
• If we order 30,000 units, the minimum payoff would be $1400
• If we order 40,000 units, the minimum payoff would be ($1600)

The highest minimum payoff arises when we order 10,000 units. This ensures that the worst possible scenario still results in a gain of at least $5000.

d. MINIMAX REGRET

The minimax regret strategy is the one that minimises the maximum regret. It is useful for a risk-neutral decision maker.

'Regret' in this context is defined as the opportunity loss through having made the wrong decision.

Regret table would be as follows

Looking at the regret table.

• If we order 10,000 units, the maximum regret would be $11800
• If we order 20,000 units, the maximum regret would be $9200
• If we order 30,000 units, the maximum regret would be $3600
• If we order 40,000 units, the maximum regret would be $6600

Thus the least regret is when we order 30,000 units.

e. Expected value decision

An expected value is a weighted average of all possible outcomes where weights are the probabilities of each outcome.

Thus Order should be = 13000 * 0.2 + 19000 * 0.4 + 28000 * 0.25 + 36000 * 0.15 = 22600 units

However since the ponchos can be ordered in a pallet of 10000 units only, we should order either 20000 units or 30000 units

• If 20000 units are ordered and demand turns out to be 22600, payoff = 20000 * 0.5 = $10,000
• If 30000 units are ordered and demand turns out to be 22600, payoff = 22600 * 0.5 - 7400 * 0.3 = $9080

Thus 20,000 units of ponchos should be ordered.

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