Consider the following problem. Maximize Z = 5x1 + 3x2 + 4x3, Subject to 2x1 + x2 + x3 ≤ 20 3x1 + x2 + 2x3 ≤ 30
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Please do not give solution in image formate thanku.
Consider the following problem.
Maximize Z = 5x1 + 3x2 + 4x3,
Subject to
2x1 + x2 + x3 ≤ 20
3x1 + x2 + 2x3 ≤ 30
and
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
You are given the information that the non-zero variables in the optimal solution are x2 and x3.
Describe how you can use this information to adapt the simplex method to solve this problem in the minimum possible number of iterations (when you start from the usual initial BF solution). Do not actually perform any iterations.
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- Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60The model in Example 9.3 has only two market outcomes, good and bad, and two corresponding predictions, good and bad. Modify the decision tree by allowing three outcomes and three predictions: good, fair, and bad. You can change the inputs to the model (monetary values and probabilities) in any reasonable way you like. Then you will also have to modify the Bayes rule calculations. You can decide whether it is easier to modify the existing tree or start from scratch with a new tree.You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
- When you use a RISKSIMTABLE function for a decision variable, such as the order quantity in the Walton model, explain how this provides a fair comparison across the different values tested.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.
- 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?STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 32 Vidhya Balan is planning to liquidate her investments inmutual funds and invest in real estate. Before makingthe change to her investment strategy, Vidhya wants toforecast the price of mutual funds for the next 2 months.She has collected the following data on the average fundprices for the past 10 months.Month Average Fund Price1 55.12 53.83 53.44 52.955 52.156 52.757 52.658 51.59 52.2510 51.7a Using a five-period moving average, forecast theaverage fund price for Period 11.b. Using exponential smoothing with α = 0.3 forecastthe average fund price for Period 11. Assume an initialforecast for Month 2 (F2) as 55.10
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2WHAT 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 ABOVECAN YOU EXPLAIN THREE OUTPUTS OF MARTRIX MODEL CONNNNUNICATION WITH SOME EXAMPLES?