Quiz#3-F.doc

General Directions:

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Use the conventional form of variables: decision variables (X1, X2, X3, . . .) deviational variables (d1, d2, d3, . . .) states-of-nature (s1, s2, s3, . . .) Define all variables used Maintain at least 8 decimal places

1. The city council of a small town has decided to build a tennis court in the central park. Players are expected to arrive on the average of 10 sets of players per 12-hour day. Playing time is exponentially distributed with a mean of one hour. Arrivals are Poisson. However, a member of the city council contends that people will not wait if two groups are already waiting. Determine the necessary statistical data and make a recommendation based on these. 2. The president of a large oil company must decide how to invest the company’s P10 million of excess profits. He could invest the entire sum in solar energy research, or he could use the money to research better ways of processing coal so that it will burn more cleanly. Another possible option is to put half of this R&D money into solar research and half into coal research. The president estimates 1,000 percent return on investment if the solar research is successful and a 500 percent return on investment if the coal research is successful. 2.1. Construct a payoff table for the president’s R&D investment problem. 2.2. Based on the maximin criterion, what decision should the president make? 2.3. Based on the maximax criterion, what decision should the president make? 2.4. Based on the minimax regret criterion, what decision should the president make?

3. The HO Corporation is considering six R & D projects for the next fiscal year. It has allocated P250,000 for research and development projects. All projects must be completely funded or not funded at all. Given the expected rate of return for the six projects in the table below, formulate a mathematical model to maximize the return from the R & D projects. Then, using the Branch & Bound method, determine which projects would be funded and what will be the maximum return. Project 1 2 3 4 5 6

Rate of Return 20% 23% 30% 15% 18% 25%

Cost P 80,000 50,000 40,000 70,000 80,000 60,000

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