Question

I posted five questions. The last one is a yes or no. Thanks.

Fantastic Distributing is in the process of trying to determine where they should schedule next year's production of a popular line of kitchen utensils that they distribute. Manufacturers in four different countries have submitted bids to Fantastic Distributing. However, a pending trade bill in Congress will greatly affect the cost to Fantastic Distributing due to proposed tariffs, favorable trading status, etc. After careful analysis, Fantastic Distributing has determined the following cost breakdown for the four manufacturers (in $1,000's) based on whether or not the trade bill passes Bill Passes Bill Fails 210 Country A 260 320 160 Country B Country C 240 240 Country D 210 275 If Fantastic Distributing estimates that there is a 70% chance of the bill passing, which country should they choose for manufacturing? A payoff table is given as State of Nature S3 S2 S1 Decision 14 D1 17 12 12 D2 D3 If the probabilities of S1, S2 and S3 are.2,4, and 4, respectively, what is the EVPI? The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do. Which decision should be made using the minimax regret approach? State of Nature (Demand) High Decision Low Medium D1 15 25 30 D2 20 50 80 D3 25 30 50 D4 18 35 60 The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. If an optimistic strategy is used, determine which decision the company should select. State of Nature Decision S1 S2 S3 D1 50 70 30 D2 30 90 D3 80 10 20 D4 30 30 30 The Power Drink Company must decide whether or not to introduce a new diet soft drink. Management feels that if it does introduce the diet soda, it will yield a profit of $1 million if sales are around 100 million, a profit of $200,000 if sales are around 50 million, or it will lose $2 million if sales are only around 1 million bottles. If Power Drink does not market the new diet soda it will suffera loss of$400,00·Should Power Drink introduce the social, the company i,conservative?

Answer 1

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If Fantastic distribution estimates a 70% chance of the bill passing, so, failing would be 30%

Expected profit of Country A = 0.7*260 + 0.3*210 = 182 + 63 = 245

Expected profit of Country B = 0.7*320 + 0.3*160 = 224 + 48 = 272

Expected profit of Country C = 0.7*240 + 0.3*240 = 168 + 720 = 888

Expected profit of Country D = 0.7*275 + 0.3*210 = 192.5 + 63 = 255.5

It shows that the Country C would give the maximum profit, and should be chosen for manufacturing.

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EVPI of each Decision are as follows:

D1 = .2*14 + .4*9 + .4*5 = 2.8 + 3.6 + 2 = 8.4

D2 = .2*12 + .4*17 + .4*3 = 2.4 + 6.8 + 1.2 = 10.4

D3 = .2*9 + .4*5 + .4*12 = 1.8 + 2 + 4.8 = 8.6

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The regret table is as follows:

The maximum for Low is 25, Medium is 50 and High is 80.

We first find out the Maximum regret of each decision, and then choose the lowest of them to get the min-max pay-off.

	State of Nature			Maximum
Decision	Low	Medium	High
D1	10	25	50	50
D2	5	0	0	5
D3	0	20	30	30
D4	7	15	20	20

The minimum of the maximum pay-offs is 5. So, the decision D2 should be chosen based on the minmax regret strategy.

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Optimistic Approach

The optimistic approach is also known as the Maximax approach. So we first find out the maximum each decision and choose the highest pay-off.

	State of Nature
Decision	S1	S2	S3	Maximum
D1	50	70	-30	70
D2	90	30	-40	90
D3	-80	-10	20	20
D4	30	30	30	30

The maximum of the Maximum pay-off is 90. So, the decision should be to invest in D2.

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Introduction of new soft drink

NO. The Power Drink would not introduce the new soft drink as it is conservative and is risk averse. It would not want to take up the risk of introducing something new and incur a loss.