Find typical seasonal index for each quarter. Following is the probability distr

Question

Find typical seasonal index for each quarter. Following is the probability distribution for a new toy; Demand 8 10 12 14 01 0.3 0.5 0.1 Each toy costs the store $20 and store sells it for $50. Any unsold toys are salvaged at $10 each. a) Set up a conditional profit table for stock levels of 8, 10, 12, 14 and b) Using "maximax rule", "maximin rule" and "minimax regret rule" how many toys should be stocked? c) Using the expected value rule, how many toys should be stocked? A jewelry store makes necklaces and bracelets from gold and platinum. The store has 36 ounces of gold and 48 ounces of platinum. Each necklace requires 4 ounces of gold and 3 ounces of platinum, while each bracelet 3 ounces of gold and 6 ounces of platinum. Store cannot sell more than 6 bracelets. Profit from a necklace is $50 while from a bracelet is $70. How many necklaces and bracelets should the store make to maximize the total profit?

Explanation / Answer

a)

If you stock 'x' toys and sell 'y' toys ,

then for (x > y) the profit is 30x - 10y (Profit of toys sold = 50 -20 = 30, and if the toy is not sold, profit = 10 -20 = -10)

for (x = y), the profit is 30x

for (x < y) , the profit is still 30x, as you cannot sell more toys than in the stock.

(b) Maximax approach - The maxium row value is 240, 300, 360, 420. The maximum of the row values is 420. So, by maximax approach, the decision is to stock 14 toys.

Maximin approach - The minimum row value is 240, 220, 200, 180. The maximum of the row values is 240. So, by maximin approach, the decision is to stock 8 toys.

Minimax regret approach - The regret value to sell 8 toys is 0, 20, 40, 60

The regret value to sell 10 toys is 60, 0, 20, 40

The regret value to sell 12 toys is 120, 60, 0, 20

The regret value to sell 14 toys is 180, 120, 60 , 0

The maximum regret values for each rows are 180, 120, 60, 60.

The minmium value is 60 which is regret value to sell 8 or 14 toys. So the decision as per minimax regret approach is to stock 8 or 14 toys.

(c) If we buy 8 toys, expected profit = 0.1 * 30*8 + 0.3 * 30*8 + 0.5 * 30*8 + 0.1 * 30*8 = $240

If we buy 10 toys, expected profit = 0.1 * (30*8 - 10*2) + 0.3 * 30*10 + 0.5 * 30*10 + 0.1 * 30*10 = $292

If we buy 12 toys, expected profit = 0.1 * (30*8 - 10*4) + 0.3 * (30*10- 10*2) + 0.5 * 30*12 + 0.1 * 30*12 = $320

If we buy 14 toys, expected profit = 0.1 * (30*8 - 10*6) + 0.3 * (30*10- 10*4) + 0.5 * (30*12 - 10*2) + 0.1 * 30*14 = $308

Max expected profit = $320 is when we stock 12 toys.

By expected value rule, we should stock 12 toys.

Stock Demand 8 10 12 14 8 30*8 = 240 30*8 = 240 30*8 = 240 30*8 = 240 10 30*8 - 10*2 = 220 30*10 = 300 30*10 = 300 30*10 = 300 12 30*8 - 10*4 = 200 30*10 - 10*2 =280 30*12 = 360 30*12 = 360 14 30*8 - 10*6= 180 30*10 - 10*4 = 260 30*12 - 10*2 = 340 30*14 = 420

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