Profit Projections Under Four Order Scenarios$250,000.00$200,000.00$150,000.00$100,000.00$50,000.00S-$450,000.00)$(100,000.00)$(150,000.00)10000 1200 14000 16000 18000 20000 22000 24000 26000 28000 30000P(Demand ≤ Q°) =O c. 17,273O d. 21,024--Q-15,0003A common method for determining the order quantity is called the single-period inventory model. This model fits your current situation because you are making only one single order for the holiday season. The maximum expected profit in the single-inventory model is based on the following formula:cu + co8P(Demand ≤ Q¹) = 8 + 11 = 0.4211What quantity ordered (Q)corresponds to a probabilityof P-0.4211 in order tomaximze profit?where P(Demand s Q) is the probability that demand is less than or equal to the recommended order quantity, Q. The term cu is the cost per unit of underestimating demand (and losing sales because of going out of stock) and co is the cost per unit of overestimating demand (having unsold inventory). So,cu=$24- $16 $8 lost per unit if Weather Teddy runs out of stock andCu = $16 - $5 = $11 lost per unit if left-over inventory must be sold at the clearance price.ThereforeSALES (UNITS)Q-18,000 --Q-24,0000.4211Single-period Inventory Model for Weather Teddy-Q-28,0000.57891-20,000What is the optimal production / order quantity in order to maximize profit?O a. 18,980O b. 22,6532 Case Problem: Specialty ToysYou are an inventory specialist for Specialty Toys, Inc. The company sells a variety of new and innovative children's toys. You know that the preholiday season is the best time to introduce a new toy because many families use this time to look for new ideas forDecember holiday gifts. When the company discovers a new toy with good market potential, it chooses an October market-entry date.For you to get toys in your stores by October, you place one-time orders with manufacturers in June or July of each year. You are aware that demand for children's toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace oftenincreases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving the company stuck with high levels of inventory that must be sold at reduced prices.The most important question you face is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If you order too few, sales will be lost; if you order too many, profits will be reduced because of low prices offered in clearancesales.For the coming season, the company plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear will make weather predictions using an internal barometer when its hand is pressed. Tests show the toy's weather predictions are quitegood as compared to local television forecasters.The sales department has given you the following sales forecast information:.025Weather Teddy Sales Forecast in Units10,000.95A = 20,00030,000.025The cost of goods sold for a Weather Teddy is $16. Your company sells the bears at a retail price of $24, for a profit of $8 per unit. However, any Teddys that are not sold during the holiday season are to be quickly sold at a clearance price of $5 for a loss of $11 perunit.For reference, the following graph charts expected profits under sales scenarios ranging from 10,000 units to 30,000 units in 2,000 unit increments and four order scenarios: Q = 15,000; 18,000; 24,000; and 28,000 respectively.

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Answer) The given problem describes the application of the single-period inventory model to…