1. Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 12 hours of labor, while deluxe desks require 62 feet of pine, 18 square feet oak, and 18 hours of labor. For the next week, the company has 5000 square feet of pine, 700 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $75 while deluxe desks net a profit of $160. All desks can be sold to national chains such as Staples or Office Depot. a) Develop a linear optimization model to determine how many of each the company should make next week to maximize profit contribution. b) Implement your model on a spreadsheet and find an optimal solution. c) Explain the reduced costs associated with standard desks. d) What constraints are binding? Explain how the shadow price can be used to make decisions that will improve profitability. e)If 25% of the oak is deemed to be cosmetically defective, how will the optimal solution be affected? f) The shop foreman is suggesting that his workforce be allowed to work an additional 100 hours at an overtime premium of $6/hr. Is this a good suggestion? Why or why not? 2. The international chef, Inc. markets 3 blends of tea: premium, Duke Grey, and breakfast. The firm uses tea leaves from India,China, and new domestic California sources. Net profit per pound for each blend is $0.50 for premium, $0.30 for Duke Grey, and $0.20 for breakfast. The firm's regular weekly supplies are 20,000 lbs of Indian tea leaves, 22,000 lbs of Chinese, and 16,000 of California. Develop and solve a linear optimatization model to determine the optimal mix to maximize profit and write short memo to the president, explaining the sensitiviy infor in a language she can understand. Table: tea leaves percent quality indian chinese California Premium 40 20 20 Duke Grey 20 30 40 Breakfast 40 40 40