RCH520 Quantitative Analysis

Problem 11-15 (Algorithmic) Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of six calls per hour. On average, it takes 8.5 minutes for a consultant to answer a customer’s questions. The service time follows an exponential probability distribution. To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on customer service? Would two technical consultants enable Ocala to meet its service guidelines (no more than 35% of all customers having to wait for technical support and an average customer waiting time of two minutes or less)? Round your answers to two decimal places. With two consultants, fill in the blank % of customers have to wait, with an average waiting time of fill in the blank minutes. Therefore, two consultants Meet service goals. Problem 11-19 (Algorithmic) All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has two screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival rate is 3.6 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. a. The facility manager’s goal is to limit the average number of passengers waiting in line to 7 or fewer. How many screening stations must be open in order to satisfy the manager’s goal? Having 2 station(s) open satisfies the manager’s goal to limit the average number of passengers in the waiting line to at most 7. b. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places. W = fill in the blank minutes Problem 11-21 (Algorithmic) Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.1 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan’s management would like to evaluate two alternatives: • • Use one consultant with an average service time of 8 minutes per customer. Expand to two consultants, each of whom has an average service time of 10 minutes per customer. If the consultants are paid $13 per hour and the customer waiting time is valued at $20 per hour for waiting time prior to service, should Agan expand to the two-consultant system? Yes What is the total cost for each scenario? Round your answers to the nearest cent. The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $ fill in the blank . The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $ fill in the blank . Note: Use P0 values from Table 11.4 to answer the questions below. Problem 11-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour. a. How many extension lines should be used if the company wants to handle 85% of the calls immediately? 3 lines should be used b. What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places. L = fill in the blank c. What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places. 32.99 % Problem 13-07 (Algorithmic) Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: Demand a. Staffing Options High Medium Low Own staff 625 500 400 Outside vendor 850 650 350 Combination 600 400 300 If the demand probabilities are 0.4, 0.25, and 0.35, which decision alternative will minimize the expected cost of the data processing operation? Combination What is the expected annual cost associated with that recommendation? If required, round your answer to the nearest thousand of dollars. Expected annual cost = $ fill in the blank b. Construct a risk profile for the optimal decision in part (a). Cost Probability fill in the blank 3 fill in the blank 4 fill in the blank 5 c. d. 0.4 0.25 0.35 1.0 A graphical representation of the risk profile is also shown: What is the probability of the cost exceeding $550,000? If required, round your answer to two decimal places. Probability = fill in the blank Problem 13-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 7 Medium complex, d2 14 5 Large complex, d3 20 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for the weak demand was greater than or equal to -$19 million. a. Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places. The payoff for the medium complex under strong demand remains less than or equal to $ fill in the blank million, the large complex remains the best decision. b. Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places. The payoff for the small complex under strong demand remains less than or equal to $ fill in the blank million, the large complex remains the best decision. Problem 13-21 (Algorithmic) A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: State of Nature a. Rezoning Approved Rezoning Not Approved Decision Alternative S1 S2 Purchase, d1 640 -200 Do not purchase, d2 0 0 If the probability that the rezoning will be approved is 0.5, what decision is recommended? Recommended decision = Purchase What is the expected profit? Expected profit = $ fill in the blank thousands. b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows: Let H = High resistance to rezoning L = Low resistance to rezoning P(H) = 0.51 P(S1 | H) = 0.16 P(S2 | H) = 0.84 P(L) = 0.49 P(S1 | L) = 0.85 P(S2 | L) = 0.15 c. What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision? d. High resistance: Do not purchase e. Low resistance: Purchase f. If the option will cost the investor an additional $10,000, should the investor purchase the option? Yes, because the expected value of the option is more than the cost of the option. What is the maximum that the investor should be willing to pay for the option? Round your answer to three decimal places. Why or why not? EVSI = $ fill in the blank thousands. Problem 13-27 (Algorithmic) In a certain state lottery, a lottery ticket costs $5. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies: State of Nature Decision Alternatives Purchase Lottery Ticket, d1 Do Not Purchase Lottery Ticket, d2 a. Win Lose s1 s2 600000 -5 0 0 A realistic estimate of the chances of winning is 1 in 230,000. Use the expected value approach to recommend a decision. If required, round your answer to two decimal places. If the amount is zero enter “0”. Recommended decision: Do Not Purchase Lottery Ticket Expected Value = $ fill in the blank b. If a particular decision maker assigns an indifference probability of 0.00001 to the $0 payoff. Would this individual purchase a lottery ticket? Decision: No, Do Not Purchase Lottery Ticket Use expected utility to justify your answer. If required, round your answer to five decimal places. Expected Utility = fill in the blank The input in the box below will not be graded but may be reviewed and considered by your instructor.

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