Solution to Case Problem Specialty Toys

Solution to Case Problem Specialty Toys 10/24/2012 I. Introduction The Specialty Toys Company faces a challenge of deciding how many units of a new toy should be purchased to meet pass judgment sales demand. If too few are purchased, sales go away be lost if too many are purchased, profits will be reduced because of low prices realized in clearance sales. Here, I will help to analyze an appropriate order beat for the company. II. Data compendium 1. 20,0 00 .025 10,0 00 30,0 00 .025 .95 20,0 00 .025 10,0 00 30,0 00 .025 .95 Since the expected demand is 2000, thus, the mean is 2000.Through Excel, we reduce the z value presumption a 95% probability is 1. 96. Thus, we have z= (x-)/ ? =(30000-20000)/ ? =1. 96, so we get the standard deviation ? =(30000-20000)/1. 96=5102. The sketch of distribution is above. 95. 4% of the value of a normal random variable are within nonnegative or minus two standard deviations of its mean. 2. At order quantity of 15,000, z= (15000-20000)/5102=-0. 9 8, P(stockout) = 0. 3365 + 0. 5 = 0. 8365 At order quantity of 18,000, z= (18000-20000)/5102=-0. 39, P(stockout) = 0. 1517 + 0. 5= 0. 6517 At order quantity of 24,000, z= (24000-20000)/5102=0. 8, P (stockout) = 0. 5 0. 2823 = 0. 2177 At order quantity of 28,000, z= (28000-20000)/5102=1. 57, P (stockout) = 0. 5 0. 4418 = 0. 0582 3. regularise measure = 15,000 Unit gross revenue Total Cost gross sales at $24 gross sales at $5 Profit 10,000 240,000 240,000 25,000 25,000 20,000 240,000 360,000 0 120,000 30,000 240,000 360,000 0 120,000 Order Quantity = 18,000 Unit Sales Total Cost Sales at $24 Sales at $5 Profit 10,000 288,000 240,000 40,000 -8000 20,000 288,000 432,000 0 144,000 30,000 288,000 432,000 0 144,000Order Quantity = 24,000 Unit Sales Total Cost Sales at $24 Sales at $5 Profit 10,000 384,000 240,000 70,000 -74,000 20,000 384,000 480,000 20,000 116,000 30,000 384,000 576,000 0 192,000 Order Quantity =28,000 Unit Sales Total Cost Sales at $24 Sales at $5 Profit 10,000 448, 000 240,000 90,000 -118,000 20,000 448,000 480,000 40,000 72,000 30,000 448,000 672,000 0 224,000 4. According to the background information, we get the sketch of distribution above. Since z= (Q-20,000)/5102 =0. 52, so we get Q=20,000+0. 2*5102=22,653. Thus, the quantity would be ordered under this insurance is 22,653. The projected profits under the three sales scenarios are downstairs Order Quantity =22,653 Unit Sales Total Cost Sales at $24 Sales at $5 Profit 10,000 362,488 240,000 63,265 -59,183 20,000 362,488 480,000 13,265 130,817 30,000 362,488 543,672 0 181,224 5. From the information we get above, I would recommend an order quantity that apprize maximize the expected profit, and it can be calculated by the verbal expression below P(Demand