1. Between 10,000 units and 30,000 units the Mean (µ) would be 20, 000 units. Assuming that X represents demand for the Product with a predicted demand of 20,000 units and a 0.95 probability, the standard deviation (%u01A1):P (10,000<X<20,000) =0.95 P (10,000-20,000)/%u01A1 < (X-20,000)/%u01A1 < (30,000-20,000)/%u01A1 = 0.95

(30,000-20,000)/%u01A1=1.96. 10,000/%u01A1=1.96 as shown in *figure 1*

Therefore, %u01A1= 5102.04units

2. Probability of stock out with an order of K units is Z= (K-20000)/5102).Where Z is the normal standard.

For 15,000, Z= (15000-20000)/5102= -0.9800. P= (Z>-0.9800) = 0.8365. This tells that there is 83.65% chance for the company to run out of the product at 15,000 units. For 18,000, Z= (18000-20000)/5102= -0.3920. P= (Z>-0.3920) = 0.6525. This tells that there is 65.25% chance for the company to run out of the product at 18,000 units.

For 24,000, Z= (24000-20000)/5102= 0.7840. P= (Z>0.784) = 0.2165. This tells that there is 21.65% chance for the company to run out of the product at 24,000 units. For 28,000, Z= (28000-20000)/5102= 1.5680. P= (Z>1.5680) = 0.058. This tells that there is 5.80% chance for the company to run out of the product at 28,000 units.

3. Computation for Projected Profit is as follows:

15,000 units at a cost of $16/unit = $240,000 was invested total. In Worst case: 10000 x 24 + 5000 x 5 = $265,000 a Profit of $25,000.In Most likely: 15000 x 24 = $360,000 a Profit of $120,000.Best case: 15000 x 24 = $360,000 a Profit of $120,000. 18,000 units at a cost of $16/unit = $288,000 was invested totals. In Worst case: 10000 x 24 + 5000 x 5 = $265,000 a Loss of $23,000.In Most likely: 18000 x 24 = $432,000 a Profit of $144,000.Best case: 18000 x 24 = $432,000 a Profit of $144,000. 24,000 units at a cost of $16/unit = $384,000 was investment totals. In Worst case: 10000 x 24 + 5000 x 5 = $265,000, a Loss of $119,000.In Most likely: 20000 x 24 + 4000 x 5 = $500,000, a Profit of $116,000.Best case: 24000 x 24 = $576,000, a Profit of $192,000

28,000 units at a cost of $16/unit = $448,000 was investment totals. In Worst case: 10000 x 24 + 5000 x 5 = $265,000, a Loss of $183,000.In Most likely: 20000 x 24 + 4000 x 5 = $500,000, a Profit of $52,000.Best case: 28000 x 24 = $672,000, a Profit of $224,000

4. For the order quantity to meet 70% demand, following should be done:

P (Z < (K-20000)/5102) = 0.70.

(K-20000)/5102 = 0.5244.

K = 20000 + 5102 * 0.5244 = 20000 + 2675

K= 22,675 units to be ordered

5. In the Best Case, the Expected Sales Price is 22,675 * 24 = $544,200. The suggested order quantity is 22,675, therefore the Cost is 22, 675*16 = $362,800. Sales are expected to be 30,000 so there is no stock out as the projected profit is 544, 200 – 362,800 = $181,400.

In the Most Likely Case Scenario the Expected Sale Price = 544,200, the Cost is 22,675 * 16 = 362,800. There is no stock out in this case as the Projected profit = 544,200 – 362,800 = $181,400.

In the Worst Case Scenario the Expected sales = 10,000 * 24 = $240,000 as based on sell at $24 on cost of $16 per unit. The expense is 22,675 * 16 = $362,800. Stock out is 12,675 units (22, 675– 10, 000). These will be sold at $5 per unit = 12,675 *5 = $63,375, Total sale price = 240,000 + 63,375 = $303,375, Projected profit = 362,800 – 303,375 = $59,425.

Orders between 15,000 to 18,000 units should be requested because there will be realized profits, even in the worst scenarios.