Lucy lives in Comfort and makes a living selling specialized items during various seasons of the year. This winter she plans to sells certain hand-crafted winter outfit. She will buy the outfit from a farmers’ cooperative (“the Co-op”) in a border town in Texas. The Co-op sells the outfit in bales, with each bale containing 1,500 outfits. Ordinarily, the Co-op charges $60,000 for each bale (i.e., $40 each outfit). However, to encourage large volume purchases, the Co-op discounts the price to $57,000 a bale (i.e., $38 each outfit) for customers who buy two bales, and discounts the price even further to $51,000 a bale (i.e., $34 each outfit) for customers who buy three or more bales. On the other hand, to discourage piecemeal purchases, the Co-op charges the retail price of $50 per outfit for piecemeal purchases but delivers such orders free of shipping & handling costs.
Lucy plans to retail the outfit in Comfort for $50 apiece and must decide the quantity to buy. A concern she has with this outfit as with all seasonal goods is that she does not know whether it will be a hit or a flop. The only thing she can think of is that demand for it may be real low, which he puts at 1,200 or low, which she puts at 2,000 units or modest, which she puts at 3500 or high, which she put at 4,000. For this reason, she considers buying a bale (1,500 outfits), two bales (3,000 outfits), or three bales (4,500 outfits). In evaluating her options, she is aware that she must auction any unsold units at the end of the season for half price (i.e., for $25 apiece) in an “end-of-season” clearance sale. This is because seasonal fashion outfits hardly sell in subsequent seasons.
Another strategy she plans to put in place is an “out-of-stock” deal to be advertised, offering to rush-order and sell the outfit for $45 to anyone who visits the store for the outfit and finds the store to be out of it. She knows, however, that every such transaction will cost her $5 as she must buy such orders at the retail price of $50 apiece.
Required:
1. If he buys 1500 wears, compute the contribution margin at each of the four possible demand levels
2. If he buys 3000 wears, compute the contribution margin at each of the four possible demand levels
3. If he buys 4500 wears, compute the contribution margin at each of the four possible demand levels
4. Using the maximin rule, select the most attractive of the three purchase actions he is considering
5. Using the maximax rule, select the most attractive of the three purchase actions he is considering
6. Using the minimax-regret rule, compute the maximum regret under each purchase action and select the purchase decision that should be most attractive of the three based on the minimax-regret rule.
7. Assume that, with the help of his statistician friend, Lucy assigns a probability distribution to the summer demand as follows: 0.08 for real low demand, 0.22 for low demand, 0.45 for modest demand, and 0.25 for high demand. Compute the expected contribution margin for each of the three purchase actions and use the expected value criterion to select the best of the three purchase actions.