1. Bothers John and Jason Rogers are trying to establish Illinois RiverHawk Floats to offer rafts for customers to float the Illinois River. 50 rafts are leased from a supplier for a monthly (30 days) cost of $415 per raft. The rafts are rented to customers for $25 per day. Customer demand follows a normal distribution, with a mean of 50 rafts and standard deviation of 8.5 rafts. (Make all demands integers in the model). If all 50 rafts are rented out, customers are referred to another outfitter who has a working relationship with the brothers. a. Set up the model and simulate a month (30 days) of operation to calculate the total monthly profit b. Replicate the simulation for 5 months (the expected float season) and determine the average total monthly profit. Note: this does not mean make 5 copies of the model. Run it 5 times, record and use the results appropriately.
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- D & R A1 10 - 8 Question 10. Minimum Variance Commodity Hedge Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton. What is the profit from this hedged position if the spot cocoa price in three months turns out to be $3,100?D & R A1 10 - 9 Question 10. Minimum Variance Commodity Hedge Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton. Calculate the gain/loss on spot position, the gain/loss on futures position, and the profits from this hedged position by hypothesizing…4.7 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 Staffing Options High Medium Low Own staff 650 650 600 Outside vendor 900 600 300 Combination 800 650 500 If the demand probabilities are 0.2, 0.5, and 0.3, and the table below shows the total cost of the different options, construct a risk profile for the optimal decision in the table. Option Total Cost Own Staff 635 Outside Vendor 570 Combination 635
- 4.25 The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. Use a decision tree to recommend a decision.Recommended decision: Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.EVPI: $After analyzing the costs of various options for obtaining brackets, Ross White (see Problems 6-27 through 6-29) recognizes that although he knows that the lead time is 2 days and the demand per day averages 10 units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of 1.5 units. What Z value would be appropriate for a 98% service level? What safety stock should Ross maintain if he wants a 98% service level? What is the adjusted ROP for the brackets? What is the annual holding cost for the safety stock if the annual holding cost per unit is $1.50?Risk-neutral Icarus Airlines must commit now to leasing 1, 2, or 3 new airplanes. It knows with certainty that on the basis of business travel alone, it will need at least 1 airplane. The marketing division says that there is a 50% chance that tourism will be big enough for a second plane only. Otherwise, tourism will be big enough for a third plane. This, plus revenue information, yields the following table: Planes Tourism Revenue Expected Leased Light Heavy Profit 2 $90 million $60 million $75 million 3 $10 million $110 million $60 million Without additional information, Icarus Airlines would Select one: A. lease 2 airplanes in order to guarantee it avoids the worst outcome, $10 million B. lease 3 airplanes because $110 million is greater than $90 million C. lease 2 airplanes because $75 million is greater than $60 million. D. lease 3 airplanes because $60 million is greater than $10 million.
- 9 10 11 12 answer only1 . Individual Problems 17-2 You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is . Given that this is , you play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is . (Hint: At what probability does playing the final round yield an expected value of zero?)(Ch 7) A large number of MBA applicants are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. Now, we can apply inverse normal to find the top 2.5 percent of the applicants score at least about ____. a. 606 b. 600 c. 617 d. 646
- 8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow.s1 s2 s3d1 500 100 -400d2 200 150 100d3 -100 200 300probability.2 .6 .2Indifference Probability for PersonPayoff A B C300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89 .60 .22-100 .75 .45 .10a. Plot the utility function for each decision maker.b. Characterize each decision maker's attitude toward risk.c. Which decision will each person prefer?Tom is a salesman. The following are the details regarding source of his income. Base weekly salary = $350 Sales commission = 12% of price the item sold Average price of items sold = $270 Average weekly number of items sold, E(x) = 30 Standard deviation of number of items sold per week, sd(x) = 6.8 Number of weeks a year Tom works = 48 25 Tom's average annual earnings is ________. a $65,042 b $63,456 c $61,908 d $60,398Betty runs a toy store. Each toy costs Betty $4 and sells for $10 (so the gross profit per unit sold is $6). Daily demand varies according to the following table: Demand Probability 90 0.64 100 0.24 110 0.12 At the beginning of every day, Betty replenishes shelves with 100 toys (i.e., there are 100 toys for sale every day). If daily demand is less than 100, an inventory holding cost of $0.10 is charged for each toy that is not sold. However, if daily demand is greater than 100, a stockout occurs, and a shortage cost of $0.90 is charged for each unit of demand that cannot be satisfied. Unsatisfied demand is lost. (a) Set up intervals of random numbers that can be used to simulate daily demand. (b) Sketch a simulation table and perform a simulation for 9 days. Use the random numbers 0.76, 0.26, 0.77, 0.57, 0.87, 0.35, 0.50, 0.56, and 0.90 to generate simulated values for daily demand for those 9 days. Based on this sample of 9 days, what is the average daily net profit and service level…