Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4, Problem 61P
Summary Introduction
To develop: An linear programming model so that the investor can achieve the goal.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
9) Today is your 20th birthday. Your parents just gave you $5,000 that you plan to use to open a stock brokerage account. Your plan is to add $500 to the account each year on your birthday. Your first $500 contribution will come one year from now on your 21st birthday. Your 45th and final $500 contribution will occur on your 65th birthday. You plan to withdraw $5,000 from the account five years from now on your 25th birthday to take a trip to Europe. You also anticipate that you will need to withdraw $10,000 from the account 10 years from now on your 30th birthday to take a trip to Asia. You expect that the account will have an average annual return of 12 percent. How much money do you anticipate that you will have in the account on your 65th birthday, following your final contribution?
Use excel for this problem
A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return.
Bond
Annual Return
Maturity
Risk
Tax
Free
A
9.5%
Long
High
Yes
B
8.0%
Short
Low
Yes
C
9.0%
Long
Low
No
D
9.0%
Long
High
Yes
E
9.0%
Short
High
No
The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free.
Formulate the LP model for this problem.
Create the spreadsheet model and use Solver to solve the problem.
A few years ago, Michael purchased a home for $394,000. Today, the home is worth $520,000. His remaining mortgage balance is $166,000. Assuming Michael can borrow up to 80 percent of the market value of his home, what is the maximum amount he can borrow?
Chapter 4 Solutions
Practical Management Science
Ch. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10P
Ch. 4.3 - Prob. 11PCh. 4.3 - Prob. 12PCh. 4.4 - Prob. 13PCh. 4.4 - Prob. 14PCh. 4.4 - Prob. 15PCh. 4.4 - Prob. 16PCh. 4.4 - Prob. 17PCh. 4.4 - Prob. 18PCh. 4.4 - Prob. 19PCh. 4.5 - Prob. 20PCh. 4.5 - Prob. 21PCh. 4.5 - Prob. 22PCh. 4.5 - Prob. 23PCh. 4.5 - Prob. 24PCh. 4.5 - Prob. 25PCh. 4.6 - Prob. 26PCh. 4.6 - Prob. 27PCh. 4.6 - Prob. 28PCh. 4.6 - Prob. 29PCh. 4.7 - Prob. 30PCh. 4.7 - Prob. 31PCh. 4.7 - Prob. 32PCh. 4.7 - Prob. 33PCh. 4.7 - Prob. 34PCh. 4.7 - Prob. 35PCh. 4.7 - Prob. 36PCh. 4.7 - Prob. 37PCh. 4.7 - Prob. 38PCh. 4.7 - Prob. 39PCh. 4.7 - Prob. 40PCh. 4.8 - Prob. 41PCh. 4.8 - Prob. 42PCh. 4.8 - Prob. 43PCh. 4.8 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 62PCh. 4 - Prob. 63PCh. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - Prob. 80PCh. 4 - You want to take out a 450,000 loan on a 20-year...Ch. 4 - Prob. 82PCh. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - Prob. 85PCh. 4 - Prob. 86PCh. 4 - Prob. 87PCh. 4 - Prob. 88PCh. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - Prob. 98PCh. 4 - Prob. 99PCh. 4 - Prob. 100PCh. 4 - Prob. 101PCh. 4 - Prob. 102PCh. 4 - Prob. 103PCh. 4 - Prob. 104PCh. 4 - Prob. 105PCh. 4 - Prob. 106PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 111PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 115PCh. 4 - Prob. 116PCh. 4 - Prob. 117PCh. 4 - Prob. 118PCh. 4 - Prob. 119PCh. 4 - Prob. 120PCh. 4 - Prob. 121PCh. 4 - Prob. 122PCh. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Prob. 126PCh. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - Prob. 132PCh. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?arrow_forwardMy current income is $40,000. I believe that I owe$8,000 in taxes. For $500, I can hire a CPA to review mytax return; there is a 20% chance that she will saveme $4,000 in taxes. My utility function for (disposableincome) (current income) (taxes) (payment toaccountant) is given by x where x is disposable income.Should I hire the CPA?arrow_forwardSuppose we have a stock with the following information: Dividend Next year: $ 5.00 Dividend growth rate: 6.00% Required return: 15.00% With this growth rate, the dividend next year will be: So, the stock price today with the constant dividend growth model is: Stock price today: The constant dividend growth equation is the present value of a growing perpetuity, but we should cautio same information from above, we can calculate the stock price for various growth rates. g 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% Stock pricearrow_forward
- A firm has 30 million shares outstanding, and each share is traded at $100. In this case, the market capitalization is 30,000 shares, that is, 30 million shares/$100 $200,000, that is, $2,000 × $100. $3 billion, that is, 30 million shares × $100. 20:1, that is, $2,000/$100.arrow_forwardThere are three investments, B1, B2 and B3. All of them have the same expected value and each with two possible payoffs. The payoffs from investment B1 are independent from payoffs from B2 and B3. The payoffs from B2 and B3 are perfectly negatively correlated, which means that when B2 has a high payoff, B3 has a low payoff, and vice versa. An investor has only $800 to invest. Find the investment strategy that minimizes the risk. Hint: It may be easier to think of the following situation. Let events F and G be independent. The following is given: Payoff from investing $100 in either B2 or B3 В $100 $140 Cases B3 Probability event F happens event F does not happen $140 $100 0.5 0.5 and Payoff from investing $100 in BỊ Cases В Probability $100 event G happens event G does not happen $140 0.5 0.5arrow_forwardSuppose that you want to invest $10,000 in the stock market by buying shares in one of two companies: A and B. Shares in company A though risky, could yield a 50% return on investment during the next year. If the stock market if conditions are not favorable (bear market) the stock may lose 20% of it value. Company B provides safe investments with 15% return in a bull market and only 5% in a bear market Ali the applications you have consulted are predicting a 60% chance for a bull market and 40% for a bear market. Where you invest your money? Construct a decision tree.arrow_forward
- Please zoom it for clere imagearrow_forwardForrester and Cohen is a small accounting firm managed by Joseph Cohen since the retirement in December of his partner, Brenda Forrester. Cohen and his 3 CPAS together bill 620 hours per month. When Cohen or another accountant bills more than 155 hours per month, he or she gets an additional "overtime" pay of $63.20 for each of the extra hours. This is above and beyond the $4,900 salary each draws during the month. (Cohen draws the same base pay as his employees.) Cohen strongly discourages any CPA from working (billing) more than 250 hours in any given month. The demand for billable hours for the firm over the next 6 months is estimated below. attempted Cohen has an agreement with Forrester, his former partner, to help out during the busy tax season, up to 250 hours in any given month if needed, for an hourly fee of $135. Cohen will not even consider laying off one of his colleagues in the case of a slow economy. He could, however, hire another CPA at the same salary as business…arrow_forwardYou have $50,000 to invest in three stocks. Let Ri be the random variable representing the annual return on $1 invested in stock i. For example, if Ri = 0.12, then $1 invested in stock i at the beginning of a year is worth $1.12 at the end of the year. The means are E(R1) = 0.17, E(R2) = 0.15, and E(R3) = 0.12. The variances are Var R1 = 0.25, Var R2 = 0.18, and Var R3 = 0.14. The correlations are r12 = 0.6, r13 = 0.9, and r23 = 0.7. Determine the minimum-variance portfolio that attains a mean annual return of at least 0.14. If needed, round your answers to three decimal digits. Investment decision Stock 1 Stock 2 Stock 3 Fractions to investarrow_forward
- Forrester and Cohen is a small accounting firm managed by Joseph Cohen since the retirement in December of his partner, Brenda Forrester. Cohen and his 3 CPAs together bill 640 hours per month. When Cohen or another accountant bills more than 160 hours per month, he or she gets an additional "overtime" pay of $62.50 for each of the extra hours. This is above and beyond the $5,000 salary each draws during the month. (Cohen draws the same base pay as his employees.) Cohen strongly discourages any CPA from working (billing) more than 250 hours in any given month. The demand for billable hours for the firm over the next 6 months is estimated below. Month Jan. Feb. Mar Apr. Estimate of Billable Hours 600 490 1,010 1,220 660 570 O May June Cohen has an agreement with Forrester, his former partner, to help out during the busy tax season, up to 250 hours in any given month if needed, for an hourly fee of $120. Cohen will not even consider laying off one of his colleagues in the case of a slow…arrow_forwardGinger owns a property worth $500,000. She owes $220,000 on her mortgage. How much equity does she have in the property? 44% 82% 56% 27%arrow_forwardHome mortgage lenders often charge points on a loan in order to avoid exceeding a legal limit on interest rates or to make their rates appear competitive with those of other lenders. As an example, with a two-point loan, the lender would loan only $98 for each $100 borrowed. The borrower would receive only $98 but would have to make payments just as if he or she had received $100. In this way, the lender can make more money while keeping his or her interest rate lower. Suppose that you receive a loan of $260,000 payable at the end each month for 30 years with an interest rate of 9% compounded monthly, but you have been charged three points. What is the effective interest rate on this home mortgage loan?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,