Question 5: A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour is sensitive to three potential weather conditions: cold, mild, and warm. The following table represents the operations cost per hour for each alternative-state of nature combination: States of Nature Weather-related cost per hour Mild cost/day Alternatives EMV Cold cost/day $42 $45 $40 Warm cost/day $45 $47 $54 $48 $45 Machine 1 Machine 2 Machine 3 $40 $42 $35 Machine 4 Machine 5 $60 $45 0.3 $30 $40 0.5 0,2 Assume that for a randomly selected day, there is a 30% probability of cold weather, 50% probability of mild weather, and 20% probability of warm weather. What is the EVPI?

A quality control engineer studied the relationship between years of experience as a system control engineer and the capacity of the engineer to complete within a given time a complex control design including the debugging of all computer programs and control devices. A group of 25 engineers having widely differing amounts of experience (measured in months of experience) was given the same control design project. The results of the study are given in the following table with y 5 1 if the project was successfully completed in the allocated time and y 5 0 if the project was not successfully completed. a. Determine whether experience is associated with the probability of completing the task. b. Compute the probability of successfully completing the task for an engineer having

Question 2 Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage (hours) Annual Maintenance Expense 13 17.0 10 22.0 20 30.0 28 37.0 32 47.0 17 30.5 24 32.5 31 39.0 40 51.5 40.0 38 a. Develop the estimated regression equation that relates annual maintenance expense to weekly usage. b. Test the significance of the relationship in part (a) at .05 level of significance. C. What is your conclusion at the .05 level of significance?

There are three factories located at AR, IN, and TX respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The revenue per commodity item is $10. The weekly demand of the warehouse A and B are respectively 50 and 35 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 28, 22, and 35 units. The cost of transportation per unit is given as belows.   Cost Warehouse A Warehouse B AR 5 3 IN 6 6 TX 2 4   To maintain a good relationship with all the factories, warehouse B requires that it receives at least 40% of its product from factory in TX. Realize that it is making good profit in warehouse A, AR requires that at least 35% of its product shipped to warehouse A. Formulate (without solving) a linear programming problem to maximize the profit.