A minimization Linear Programming (LP) model with two integer decision variables x1 and x2 has an optimal solution with the objective function value of 16. If we do not restrict x1 and x2 to be integers, which of the following COULD be the new optimal objective function value?
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- In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?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.
- 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.Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.Assume that the payoff table provides cost rather than profit payoffs. What isthe recommended decision using:i. the optimistic approachii. the conservative approachiii. the minimax regret approachiv. the Laplace method
- Which of the following types of mortgage loans is presumed to feature points or fees not excending 3%, a maximum term not to exceed 30 years, and no risky features (such as negative amortization, interest-only, or balloon loans)? A) A qualified mortgage B) A conventional mortgage C) A non-qualified mortgage D) A home equity line of credit (HELOC) mortgageProblem 16-15 (Algorithmic) Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000. Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place.…Fopic 4- Linear Programming: Appli eBook Problem 9-05 (Algorithmic) Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 ounces of hot sauce. Today, Kilgore has 21 pounds of beef, 16 cups of onions, 89 ounces of Kilgore's special sauce, and 61 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today.…
- WHAT WLL HAPPEN IF THERE IS A CHANGE IS ONE OF THE OBJECTIVE FUNCTION COEFFICIENT? A. SLOPE OF THE OBJECTIVE FUNCTION LINE ALWAYS WILL CHANGE B. OPTIMAL SOLUTION ALWAYS WILL CHANGE C. ONE OR MORE OF THE DECISION VARIABLES ALWAYS WILL CHANGE D. ALL OF THE ABOVE E. NONE OF THE ABOVEA desk contains three drawers. Drawer 1 contains twogold coins. Drawer 2 contains one gold coin and one silvercoin. Drawer 3 contains two silver coins. I randomly choosea drawer and then randomly choose a coin. If a silver coinis chosen, what is the probability that I chose drawer 3?21. A retirement community restricts buyers to people 55 years and older. How will this restriction affect the value of the property? The value of the property will be higher due to the value characteristic of demand. The value of the property will be less due to the value characteristic of transferability. This restriction will not have any affect on the value of the property. The value of the property will be less due to the value characteristic of scarcity.