These items must be shared between the two sons. Write an optimization model to find a partition of these items that minimizes the difference between the values of the two parts?
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A rich person passes away, leaving the following legacy:
1- A Caillebotte picture: 25000$
2- A bust of Diocletian: 5000$
3- A Yuan dinasty chinese vase: 20000$
4- A 911 Porsche: 40000$
5- Three diamonds: 12000$ each
6- A Louis XV sofa: 3000$
7- Two very precious Jack Russell race dogs: 3000$ each (the will asserts that they may not be separated)
8- A sculpture dated 200 A.D.: 10000$
9- A sailing boat: 15000$
10- A Harley Davidson motorbike: 10000$
11- A piece of furniture that once belonged to Cavour: 13.000$.
These items must be shared between the two sons. Write an optimization model to find a partition of these items that minimizes the difference between the values of the two parts?
Carefully explain all of the decision variables, constraints, objective function, and an appropriate solving method that you would choose. You *do not* need to solve your optimization model.
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- Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?
- 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%.A. Write a document with the following information: 1. What do you expect your job to pay when you start? 2. What benefits are musts for you? 3. What benefits would you like to have even though they are not musts? 4. Include the graph you generate in step B below. B. Create a spreadsheet and a graph of life vs funds For each year of your remaining life specify the amount you plan to save/invest/withdraw that year and how much you expect that amount to increase during the year (base on actual data – typical savings interest rate, typical stock market interest rate, typical CDs, typical…). Calculate how much your funds will increase/decrease over your life and create a life (x-axis) vs funds (y-axis) plot.You have recently won the super jackpot in the WashingtonState Lottery. On reading the fine print, you discover that you have the following twooptions:a. You will receive 31 annual payments of $250,000, with the first payment beingdelivered today. The income will be taxed at a rate of 28 percent. Taxes will bewithheld when the checks are issued.b. You will receive $530,000 now, and you will not have to pay taxes on this amount.In addition, beginning one year from today, you will receive $200,000 each yearfor 30 years. The cash flows from this annuity will be taxed at 28 percent.Using a discount rate of 7 percent, which option should you select?
- Suppose you are going to receive $20,000 per year forfive years. The appropriate interest rate is 7 percent.a. What is the present value of the payments if they are in the form of an ordinaryannuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future valueif the payments are an ordinary annuity? What if the payments are an annuitydue?c. Which has the highest present value, the ordinary annuity or annuity due? Whichhas the highest future value? Will this always be true?The below is an extract from the fixed asset register of ABC Ltd as at 31 December 2019Date of PurchaseCostuseful lifeLand1-Jan-306,000,000.000Building28-Feb-172,000,000.0020Vehicle:650,000.00Toyota Hilux1-Oct-19 350,000.005Ford Ranger30-Jun-17 300,000.005Furniture and Fittings1-May-20150,000.002Activities throughout the 2020 Financial Period:1. New Machinery have been purchased on 01 April 2020 at a Cost of N$ 4000,000. The machinery has been installed on the 15 April 2020 and was available for use on the 01 May 2020. Machinery is the only property plant and equipment of the company that is measured according to the revaluation method.1.1. On the 30th of October 2020 management decided to revalue the machinery due to a drastic decline in the revenue from sale of machinery produced inventory.Net replacement cost for the machine as at the 30th of October 2020 is N$2 000 000.2. The Toyota Hilux was involved in an accident on 1 October 2020 due to the floods and was written off by the…I need help with everything, please. hint: you will need to define one variable for total funds needed; one variable for each for 2 securities. and five variables for investment in savings at the beginning of each year. The 6th year will be 1.04 times the 5th-year saving variable. Formulate the problem and submit the formulation - no need to solve 1. As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year Payment 1 190 2 215 3 240 4 285 5 315 6 460 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 4% annually) and government securities, at prices and rates currently quoted in The Wall Street…
- Solve for the future worth of each of the given series of payments: (a) $12,000 at the end of each six-month period for 12 years at 8% compounded semiannually. (b) $8,000 at the end of each quarter for 6 years at 12% compounded quarterly. (c) $6,000 at the end of each month for 5 years at 6% compounded monthly.Rollo Megabux has $1 million to invest in stocks orbonds. The percentage yield on each investment during thecoming year depends on whether the economy has a goodor a bad year (see Table 17). It is equally likely that theeconomy will have a good or a bad year.a If Rollo is risk-neutral, how should he invest hismoney?b For $10,000, Rollo can hire a consulting firm toforecast the state of the economy. The consulting firm’sforecasts have the following properties:P(good forecast|economy good) .80P(good forecast|economy bad) .20Should Rollo hire the consulting firm? What are EVSIand EVPI? Economy EconomyHas Good Has BadYear YearYield on stocks 22% 10%Yield on bonds 16% 14%Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?