Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February?
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quantitative Management ordering clothing, Please help
- Thread starter mariobro
- Start date
Let X be the number to buy. Since at the worst you can sell 50, and at the most 70, assume 50 < X < 70. We don't know yet whether X should be less or greater than 60, so we will have to consider two cases.Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February?
Every unit sold gives a profit of $30, and every unit not sold is a loss of $20.
The expectation value is the sum of P(demand) * profit/loss given that demand
First case: suppose X < 60.
Then if demand is fifty we sell 50 and scrap (X-50), and if demand is higher we sell all X that we have
E[profit] = P(50)*[X*($30) + (X-50)*(-$20)] + P(60)*X*($30) + P(70)*X*($30)
Second case, suppose X > 60
Then if demand is seventy we sell all X that we have, but if demand is lower we scrap some.
E[profit] = P(50)*[50*($30) + (X-50)*(-$20)] + P(60)*[60*($30) + (X-60)*(-$20)] + P(70)*X*($30)
Check if those expressions are correct, and solve each for maximum X