• The Gilbert Air-Conditioning Company is considering the purchase of a special shipment of portable air conditioners manufactured in Japan. Each unitwill cost Gilbert $80 and it will be sold for $125. Gilbert does not want to carry surplus air conditioners over until the following year. Thus. all surplus air conditioners will be sold to a wholesaler for $50 per unit. Assume that the air conditioner demand follows a normalprobability distribution with u = 20 and o = 8.a. What is the recommended order quantity?b. What is the probability that Gilbert will sell all units it orders?26. A popular newsstand in a large metropolitan area is attempting to determine how many copies of the Sunday paper it should purchase each week. Demand for the newspaper on Sundays canbe approximated by a normal probability distribution with u = 450 and a = 100. Thenewspaper costs the newsstand 35c a copy and sells for 50¢ a copy. The newsstand does not receive any value from surplus papers and thus absorbs a 100% loss on all unsold papers.a. How many copies of the Sunday paper should be purchased each week?b. What is the probability that the newsstand will have a stockout? c.The manager of the newsstand is concerned about the newsstand's image if the probability of stockout is high. The customers often purchase other items after coming to the newsstand for the Sunday paper. Frequent stockouts would cause customers to go to another news-stand. The manager agrees that a 50¢ goodwill cost should be assigned to any stockout.What is the new recommended order quantity and the new probability of a stockour?27. A perishable dairy product is ordered daily at a particular supermarket. The product, which costs $1.19 per unit, sells for $1.65 per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of $1 per unit. Assume that daily demand isapproximately normally distributed with u = 150 and a = 30.a. What is your recommended daily order quantity for the supermarket?b. What is the probability that the supermarket will sell all the units it orders?c. In problems such as these, why would the supplier offer a rebate as high as $1? For example, why not offer a nominal rebate of. say. 25c per unit? What happens to the supermarket order quantity as the rebate is reduced?28. A retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit.All units not sold during the regular season are sold for half the retail price in an end-of-season clearance sale. Assume that demand for the product is uniformly distributed between 200 and 800.a. What is the recommended order quantity?b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? That is, what is the probability of a stockout using your order quantity in part (a)?c.To keep customers happy and returning to the store later, the owner feels that stockouts should be avoided if at all possible. What is your recommended order quantity if the owner is willing to tolerate a 0.15 probability of a stockout?d. Using your answer to part (c), what is the goodwill cost you are assigning to a stockout?