final 2 solved spring 07 - Questions[46 points 2 points...

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Page 1 out of 7 Questions [46 points, 2 points each] 1. Solve the LP below: max 2·X + 3·Y s.t. 3·X + Y ! 24 X + 3·Y ! 24 X , Y " 0 2. Considering the LP formulation below, which of the following is false ? max 2·X + Y s.t. -X + 2·Y ! 4 X + Y ! 3 Y " 0 a) (-1,1) is a feasible solution. b) (2,1) is not an optimal solution. c) The objective function value of an optimal solution will be no less than 6. d) (1,2) is a feasible solution. e) None of the above. 3. Considering the LP formulation in (2) above, which of the following is true? a) If the objective function were x+2y then the optimal solution wouldn’t be unique. b) If x ! 0 were added then the optimal solution would change. c) If y ! 0 were removed then the feasible region would be unbounded. d) Changing any of the constraints would always result in either a different optimal solution or a different optimal objective value or both. e) None of the above. A printer manufacturer purchases 21,000 fusers for assembly annually. The carrying cost of these fusers is 15% of the unit cost of $60 per year. The fixed cost per purchase order is $3,500. 4. What is the EOQ for these fusers? EOQ = 2 " D " S H = 2 " D " S i " C = 2 " 21000 " 3500 15% " 60 = 4041.45 # 4041 fusers 5. What is the corresponding monthly total inventory cost? TC = D " C + D EOQ " S + EOQ 2 " H = 21000 " 60 + 21000 4041 " 3500 + 4041 2 " 15% " 60 = $1,296,373 6. How often should the manufacturer be placing orders for fusers? D Q = 21000 4041 = 5.2 orders/year , or an order about every 10 weeks. 7. What is the manufacturer’s maximum inventory level for fusers? 4041 Optimal Solution: (X=6 , Y=6) Objective function value = 30 Optimal Solution: (X=2/3 , Y=7/3) Objective function value = 11/3
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Page 2 out of 7 8. Suppose there is a 50% chance that, after investing $100 million in constructing a new factory, de- mand will be strong and the factory will produce an operating income stream with a present value of $150 million. Suppose also there is a 50% chance that demand will be weak and the present value of the operating income stream will be $20 million. The firm has the option to delay the decision for 1 year when demand will be known with certainty to be either strong or weak. However, delaying the factory construction for 1 year will increase costs by $30 million (because the timeframe for con- struction will be much compressed). Which of the following decisions maximizes expected revenue? i. Construct the factory now. ii. Construct the factory in 1 year. iii. Wait for 1 year and only construct the factory if demand is strong. iv. Never build the factory. v. There is not enough information given to answer the question.
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