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achieved. QUESTION [100 Marks- 50\%] Q1. Linear Programming (25 marks) The Lightingcomp Corporation manufactures two electrical products: (i) Air conditioners (ii) Large fans The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach. (25 marks) Q2. Linear Programming (25 marks) As part of a quality improvement initiative, Consolidated Technology employees complete a three-day training program on teaming and a two-day training program on problem-solving. The manager of quality improvement has required that at least 8 training programs on teaming and at least 10 training programs on problem-solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Technology uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs $10,000 and each training program on problem-solving costs $8000. (i) Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem-solving that should be offered in order to minimize total cost. (10 marks) 3 (ii) Graph the feasible region. (10 marks) (iii) Determine the coordinates of each extreme point. (2 marks) (iv) Solve the minimum cost solution. ( 3 marks) Q3. Decision Analysis ( 25 marks) The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. (i) Construct a decision tree for this problem. (10 marks) (ii) If the decision-maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the Optimistic, Conservative, and Minimax Regret approaches? (15 marks) (CLO 4, PLO 6) Q4. Decision Analysis (25 marks) Suppose a decision-maker faced with four decision alternatives and four states of nature develops the following profit payoff table. 4 (i) If the decision-maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? (5 marks) (ii) Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision-maker? Explain. (10 marks) (iii) Assume that the payoff table provides cost rather than profit payoffs. What is the recommended decision using the optimistic, conservative, and minimax regret approaches? (10 marks)