You have been a student at UDC for last three years. You have been buying and se

Question

You have been a student at UDC for last three years. You have been buying and selling used text books at UDC. You know that a text book in a Management course used during Spring 2017 will be used during Fall 2018. You buy these used text books for $20 each and sell these for $45 each. Any unsold text books are worthless. You anticipate selling 6, 7, 8 Or 9 books a) Set up a conditional profit table if you decide to buy 6, 7, 8 or 9 text books. b) How many text books you should buy according to maximax rule, maximin rule, and minimax regret rule? c) Assuming the following probability distribution of demand; Demand 6 7 8 9 Probability 0.2 0.3 0.4 0.1 How many text books you should buy to have maximum expected profit? d) What is expected value of the perfect information?

Explanation / Answer

(a) The conditional profit table is

If you buy 'x' books and sell 'y' books ,

then for (x > y) the profit is 25x - 20y (Profit of books sold = 45 -20 = 25, and if the book is not sold, profit = -20)

for (x = y), the profit is 25x

for (x < y) , the profit is still 25x, as you cannot sell more books than you buy

(b) Maximax approach - The maxium row value is 150, 175, 200, 225. The maximum of the row values is 225. So, by maximax approach, the decision is to buy 9 books.

Maximin approach - The minimum row value is 150, 130, 110, 90. The maximum of the row values is 150. So, by maximin approach, the decision is to buy 6 books.

Minimax regret approach - The regret value to sell 6 books is 0, 20, 40, 60

The regret value to sell 7 books is 25, 0, 20, 40

The regret value to sell 8 books is 50, 25, 0, 20

The regret value to sell 9 books is 75, 50, 25, 0

The maximum regret values for each rows are 75, 50, 40, 60.

The minmium value is 40 which is regret value to sell 6 books. So the decision as per minimax regret approach is to buy 6 books.

(c) If we buy 6 books, expected profit = 0.2 * 25*6 + 0.3 * 25*6 + 0.4 * 25*6 + 0.1 * 25*6 = $150

If we buy 7 books, expected profit = 0.2 * (25*6 - 20) + 0.3 * 25*7 + 0.4 * 25*7 + 0.1 * 25*7 = $166

If we buy 8 books, expected profit = 0.2 * (25*6 - 20*2) + 0.3 * (25*7 - 20) + 0.4 * 25*8 + 0.1 * 25*8 = $168.5

If we buy 9 books, expected profit = 0.2 * (25*6 - 20*3) + 0.3 * (25*7 - 20*2) + 0.4 * (25*8 - 20) + 0.1 * 25*9 = $153

Max expected profit = $168.5

(d) Expected Monetary value without information = $168.5

Expected Monetary value with information = 0.2 * 150 + 0.3 * 175 + 0.4 * 200 + 0.1 * 225 = $185

Expected value of perfect information = Expected Monetary value with information - Expected Monetary value without information

= $ 185 - $ 168.5 = $16.5

Buy Sell 6 7 8 9 6 25*6 = 150 25*6 = 150 25*6 = 150 25*6 = 150 7 25*6 - 20*1 = 130 25*7 = 175 25*7 = 175 25*7 = 175 8 25*6 - 20*2 = 110 25*7 - 20*1 = 155 25*8 = 200 25*8 = 200 9 25*6 - 20*3 = 90 25*7 - 20*2 = 135 25*8 - 20*1 = 180 25*9= 225

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