Question

Section B: Long Questions (SK2. AR1:20 marks B1: Orders for clothing from Flowers manufacturer for this year's National Day's season must be placed in August. The cost per National Day's dress is $40 while the anticipated selling price is $90. Demand is projected to be 100, 110, or 120 units. There is a 30 percent chance that demand will be 100 units, a 50 percent chance that demand will be 110 units, and a 20 percent chance that demand will be 120 units. The company believes that any leftover goods will have to be scrapped. Required: Prepare a payoff table, and calculate how many National Day's dresses should be ordered in August? [SK2:10 marks]

Answer 1

Preparing the payoff table.

We are showing the demand row wise. Supply column wise. If Demand > Supply, we don’t have to lose anything. But if Supply > Demand, the extra supplies will be scrap.

Here selling price = $90

Buying Price = $40

Purchase of 100 units = $4000

Purchase of 110 units = $4400

Purchase of 120 units = $4800

Selling 100 units = $9000

Selling 110 units = $9900

Selling 120 units = $10800

When Demand is 100, Supply is 100. We have no scrap and no less supply. Hence the profit = Selling – profit = $5000

But if demand is 100 and supply is 120, we have 20 extra units which will be scrap. Profit = selling of 100 – purchase of 120 = 9000 – 4800 = $4200

Similarly filling the payoff table:

Payoff Table:

		Daily Supply
Daily Demand	Probability	100	110	120
100	0.3	$5000	$4600	$4200
110	0.5	$5000	$5500	$5100
120	0.2	$5000	$5500	$6000

The expected demand on basis of probability is:

100*0.3 + 110*0.5 + 120*0.2 = 30 + 55 + 24 = 109

Hence number of quantities that should be ordered is: 110

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