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Question 3. Optimixing Production Mix for Outdoor Furniture Mannfacturing at Patio Paradise, Inc. Patio Paradise, Inc. is a munufacturer of outdoor furniture that offers throe different products, at lounge chair, a sectional sofin, and a dining table. The manufacturing process of these products involves two departments, cutting and assembly. Bsch product must go through both cutting and issembly processes, which hive a finited tumber of mochine hours anilable: 1000 hours for cutting and 1200 bours for assembly. Patio Paradiso, Inc. is also limited by the available material due to a shortage in supply. Currently, the company only has 2000 lbs of wood to work with. The net profit that Patio Parsdise receives from the manufacture and sale of one unit of each product is quite lucrative $3 for is tounge chalr, $3 for n sectionst sofa, and $5 for a dining table The Operations. Mannger at Patio Parndise model the problem as a Linear Program to decide on the optimal product mix to maximize its prolits and solved it with Excel to generato the following Sensitivity Analysis Report: Use the Sensitivity Regort above to answer the following questions. You must clearly show your working. (a) What is the optimal nolution? What is total profit that Patio Paradise anticipates by producing this mix? 2 of 4 Operntionis and Supply Chain Muragement (b) What is the value of ose more unit of cutting time? of nescmbly time? of wood? (c) A local diatributor has offered to sell Patio Paratise, the some ndditionnt wood for 80.70/7b. Should Patio Paradise bay it? If yes, how much would the firm's profit liscrease if they bolaght 550lbs, and used it in an optimal fashica? (d) The RED department bas been redentgring the sectional sofa to make it more profitable. If it cur sell one unit of this sofi with a unit profit of $4, is if profitable to produce wood under the new design? (e) Patio Paratise lace. has a chance to sell some of itar capacity in cutting at cont of \$1.50/bout: If it selk- 200 hours at tliat price, how will this affect profits? (f) If ethe unit profit on chairn were to decrense to $2.40, what would be the optimal solutioe and what profits would this production plan give