The management of a company is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows: Labor Transportation Cost ($) Procurement Cost Probability Probability Probability Cost ($) ($) 10 0.25 20 0.10 3 0.75 11 0.45 22 0.25 0.25 12 0.30 24 0.35 25 0.30 What is the profit per unit for the best-case scenario?
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- Software development is an inherently risky and uncertain process. For example, there are many examples of software that couldnt be finished by the scheduled release datebugs still remained and features werent ready. (Many people believe this was the case with Office 2007.) How might you simulate the development of a software product? What random inputs would be required? Which outputs would be of interest? Which measures of the probability distributions of these outputs would be most important?Assume a very good NBA team has a 70% chance of winning in each game it plays. During an 82-game season what is the average length of the teams longest winning streak? What is the probability that the team has a winning streak of at least 16 games? Use simulation to answer these questions, where each iteration of the simulation generates the outcomes of all 82 games.You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
- A common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the savings on unit costs will cover the fixed cost of the equipment. Suppose a company must make such a decision for a four-year time horizon, given the following data. Use simulation to estimate the probability that producing in house is better than outsourcing. If the company outsources production, it will have to purchase the product from the manufacturer for 25 per unit. This unit cost will remain constant for the next four years. The company will sell the product for 42 per unit. This price will remain constant for the next four years. If the company produces the product in house, it must buy a 500,000 machine that is depreciated on a straight-line basis over four years, and its cost of production will be 9 per unit. This unit cost will remain constant for the next four years. The demand in year 1 has a worst case of 10,000 units, a most likely case of 14,000 units, and a best case of 16,000 units. The average annual growth in demand for years 2-4 has a worst case of 7%, a most likely case of 15%, and a best case of 20%. Whatever this annual growth is, it will be the same in each of the years. The tax rate is 35%. Cash flows are discounted at 8% per year.W. L. Brown, a direct marketer of womens clothing, must determine how many telephone operators to schedule during each part of the day. W. L. Brown estimates that the number of phone calls received each hour of a typical eight-hour shift can be described by the probability distribution in the file P10_33.xlsx. Each operator can handle 15 calls per hour and costs the company 20 per hour. Each phone call that is not handled is assumed to cost the company 6 in lost profit. Considering the options of employing 6, 8, 10, 12, 14, or 16 operators, use simulation to determine the number of operators that minimizes the expected hourly cost (labor costs plus lost profits).The management of Brinkley Corporation is interested in using simulation to estimate the profit (in $) per unit for a new product. The selling price for the product will be $46 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated in the following table. Procurement Cost($) Probability Labor Cost ($) Probability Transportation Cost ($) Probability 10 0.25 20 0.10 3 0.75 11 0.45 22 0.25 5 0.25 12 0.30 24 0.35 25 0.30 (a) Compute profit (in $) per unit for the base-case scenario. x /unit $ 7 (b) Compute profit (in $) per unit for the worst-case scenario. x /unit $ 3 (c) Compute profit (in $) per unit for the best-case scenario. $ 12 ✓ /unit (d) Construct a simulation model to estimate the mean profit (in $) per unit. (Use at least 1,000 trials. Round your answer to two decimal places.) $ 7.12 (e) Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios? Simulation will provide a…
- The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows. ProcurementCost ($) Probability LaborCost ($) Probability Transportation Cost ($) Probability 10 0.20 20 0.15 3 0.75 11 0.45 22 0.20 5 0.25 12 0.35 24 0.35 25 0.30 Construct a simulation model to estimate the average profit (in $) per unit and the variance of the profit per unit. (Use at least 1,000 trials. Round your answer to two decimal places. Use the values you enter to make later calculations.) average$ variance What is a 95% confidence interval (in $) around this average? (Round your answers to two decimal places.) $ to $ (e) Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios? A simulation model does…A salesperson uses three different airlines. The probabilities of switching from one airline to another in consecutive flights are shown below. If the last flight was on Delta, what is the probability that the next was on American? American Delta Southwest American 0.5 0.25 0.25 Delta 0.2 0.6 0.2 Southwest 0.3 0.3 0.4 A 0.5 B 0.2 C 0.25 D 0.6The table below gives a discrete probability distribution. x Pr{X= x} 2 0.3766 8 0.2546 14 0.1728 20 0.1168 26 0 Calculate the theoretically exact mean, u , variance, sigma^2 , and standard deviation,sigma , for the distribution. Summary metrics: Enter your answer as a comma separated list to four decimal places, e.g. 0.1234, 0.2324, 0.4567, etc.
- Consider the following information for the Alachua Retirement Fund, with a total investment of $4 million. [5] Stock Investment Beta A $ 400,000 1.2 B 600,000 -0.4 C 1,000,000 1.5 D 2,000,000 0.8 The market required rate of return is 12 percent, and the risk-free rate is 6 percent. What is its required rate of return? Stock A has the following probability distribution of expected returns: [5] Probability Rate of Return 0.1 -15% 0.2 0 0.4 5 0.2 10 25 What is Stock A’s coefficient of variation? What is Stock T’s coefficient of…Implement a financial simulation model for a new product proposal and determine a distribution of profits using the provided discrete distributions for the unit cost, demand, and fixed costs. Price is fixed at $1,000. Simulate this model for 50 trials and a production quantity of 140. What is the average profit? Click here to view the discrete distributions. Click here to view a sample of 50 simulation trial results. Set up a lookup table for the unit cost. (Type integers or decimals. Do not round. Use ascending order.) Unit Cost Probability Lower Limit Upper Limit $400 0.25 $600 0.40 $700 0.15 $800 0.20 0.25 0.25 0.65 $400 $600 $700 $8002. A daily demand for loaves of bread at a grocery store is given by the following probability distribution: 100 150 0.20 0.25 200 0.30 250 0.15 300 0.10 p(x) and the cost payoff matrix (in Rs) as: Daily Demand 100 150 200 250 350 100 300 300 300 300 300 150 250 450 450 450 450 200 200 400 600 600 600 250 150 350 550 750 750 350 100 300 500 700 900 i) Determine the best daily stock of loaves of bread using the expected monetary value (EMV) criterion. ii) Determine the best daily stock of loaves of bread using the expected opportunity loss (EOL) criterion. i) How much will the decision maker spend to get additional information? Daily Stock