Exercise 1 The Addis Ababa city administration is attempting to determine the size of condominium houses...

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Exercise 1 The Addis Ababa city administration is attempting to determine the size of condominium houses to be built for medium and low class income group of its residents. Three sizes of developments considered by project planning team are small, medium, and large houses. There are three future conditions with regard to the level of demand for the houses as a result of fluctuating household income. The demand for the condominium houses can be low, medium, or high. The project team has estimated probabilities for the occurrences of high and medium demand as 0.5 and 0.3, respectively. The project team has also prepared the payoff table, expressed in revenue per 000' birr, as given below. Alternative, A States of nature, Sj High (S) Moderate (S) Large(A1) 50 70 Medium(A2 40 80 Small(A3) 90 Low (S3) 100 90 70 60 What decision would you recommend using: Exercise 2: a) EMV decision criterion b) EOL decision criterion c) Determine EVPI for the above exercise d) Suppose Scientific Marketing, Inc. would like to offer analysis that will provide certainty about demand conditions (favorable). Additional information will cost $15,000. Should the administration purchase the additional information? e) What is a decision tree? Depict decision tree analysis for the EMV decision criterion Identify the optimal decision alternative together with the value of the decision for Exercise 1 using each of the following criterion. a. Maximax (optimistic) decision criterion b. Maximin (pessimistic) c. Criterion of realism (Hurwicz) d. Equally likely (Laplace) e. Minimax regret Exercise 3 Player A is paid birr 8 if two coins turn both heads and birr 10 if two coins turn both tails. Player B is paid birr 3 when the two coins don't much, given the choice of being A or B, which one would you choose and what is your strategy? Exercise 4 Suppose a soft drink company (Company A) calculated the market share of two products against its major competitor (Company B) having three products and found out the impact of additional achievement in anyone of its products against the other. Company A A1 A2 Company B B1 B2 B3 6 7 15 20 12 10 Based on the information given above a. Determine the best strategy for company A as well as company B using graphical method b. Compute the value of the game Exercise 7 A company produces motor cycle seats. The company has two production lines. The production rate for line one is 50 seats per hour and for line two it is 60 seats per hour. The company has entered into a contract to supply 1200 seats daily to another company. Currently, the normal operation period for each line is 8 hours. The production manager of the company is trying to determine the best daily operation hours for the two lines. He sets the priorities to achieve his goals as given below: - P1: produce and deliver 1200 seats daily - P2: limit the daily overtime operation hours of line one to 3 hours - P3: Limit the daily overtime operation hours of line two to 4 hours Formulate the problem as a GP model and then solve it by using graphical method Exercise 8 Use the modified simplex method to solve the following goal programming problem Minimize Z= P1dl-+ P2D2-+ P2d3- P3d1+ St; X1+x2 +d1-d1+ =400 X1 + d2-s2+=240 X2d3d3+ 300 All variables greater than or equal to zero Exercise 1 The Addis Ababa city administration is attempting to determine the size of condominium houses to be built for medium and low class income group of its residents. Three sizes of developments considered by project planning team are small, medium, and large houses. There are three future conditions with regard to the level of demand for the houses as a result of fluctuating household income. The demand for the condominium houses can be low, medium, or high. The project team has estimated probabilities for the occurrences of high and medium demand as 0.5 and 0.3, respectively. The project team has also prepared the payoff table, expressed in revenue per 000' birr, as given below. Alternative, A States of nature, Sj High (S) Moderate (S) Large(A1) 50 70 Medium(A2 40 80 Small(A3) 90 Low (S3) 100 90 70 60 What decision would you recommend using: Exercise 2: a) EMV decision criterion b) EOL decision criterion c) Determine EVPI for the above exercise d) Suppose Scientific Marketing, Inc. would like to offer analysis that will provide certainty about demand conditions (favorable). Additional information will cost $15,000. Should the administration purchase the additional information? e) What is a decision tree? Depict decision tree analysis for the EMV decision criterion Identify the optimal decision alternative together with the value of the decision for Exercise 1 using each of the following criterion. a. Maximax (optimistic) decision criterion b. Maximin (pessimistic) c. Criterion of realism (Hurwicz) d. Equally likely (Laplace) e. Minimax regret Exercise 3 Player A is paid birr 8 if two coins turn both heads and birr 10 if two coins turn both tails. Player B is paid birr 3 when the two coins don't much, given the choice of being A or B, which one would you choose and what is your strategy? Exercise 4 Suppose a soft drink company (Company A) calculated the market share of two products against its major competitor (Company B) having three products and found out the impact of additional achievement in anyone of its products against the other. Company A A1 A2 Company B B1 B2 B3 6 7 15 20 12 10 Based on the information given above a. Determine the best strategy for company A as well as company B using graphical method b. Compute the value of the game Exercise 7 A company produces motor cycle seats. The company has two production lines. The production rate for line one is 50 seats per hour and for line two it is 60 seats per hour. The company has entered into a contract to supply 1200 seats daily to another company. Currently, the normal operation period for each line is 8 hours. The production manager of the company is trying to determine the best daily operation hours for the two lines. He sets the priorities to achieve his goals as given below: - P1: produce and deliver 1200 seats daily - P2: limit the daily overtime operation hours of line one to 3 hours - P3: Limit the daily overtime operation hours of line two to 4 hours Formulate the problem as a GP model and then solve it by using graphical method Exercise 8 Use the modified simplex method to solve the following goal programming problem Minimize Z= P1dl-+ P2D2-+ P2d3- P3d1+ St; X1+x2 +d1-d1+ =400 X1 + d2-s2+=240 X2d3d3+ 300 All variables greater than or equal to zero