Formulate an LP model for the following problems. 1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit or both. The Best Fund pays 8% per year and the time deposit pays 9%. Because the Best Fund is riskier than the time deposit, so she intends to put at most ₱30,000 into the time deposit and at least ₱10,000 into the Best Fund. How much should she allot to each investment in order to maximize her returns?

Formulate an LP model for the following problems. 1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit or both. The Best Fund pays 8% per year and the time deposit pays 9%. Because the Best Fund is riskier than the time deposit, so she intends to put at most ₱30,000 into the time deposit and at least ₱10,000 into the Best Fund. How much should she allot to each investment in order to maximize her returns?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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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%.
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
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?
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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.
The yield on 1-year Treasury securities is 6%, 2-year securitiesyield 6.2%, 3-year securities yield 6.3%, and 4-year securities yield 6.5%. There is nomaturity risk premium. Using expectations theory and geometric averages, forecast theyields on the following securities:a. A 1-year security, 1 year from nowb. A 1-year security, 2 years from nowc. A 2-year security, 1 year from nowd. A 3-year security, 1 year from now
A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.
Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…
A young engineer is considering establishing his own small company.An investment of Php 100,000 will be required which must be recovered in 15years . It is estimated that sales will be Php 150,000 per year and thatoperating expenses will be as follows:Material Php 40,000 per yearLabor Php 70,000 per yearOverhead Php 10,000 + 10% of sales/yearSelling expenses Php 5,000/yearThe young engineer will give up his regular job paying Php 150,000 per yearand devote full time to the operation of the business. This will result indecreasing labor by Php 10,000 per year , material cost by Php 7000 peryear, and overhead cost by Php 8000 per year. If the young engineer expectsto earn at least 20% on his capital, should he invest ?
Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are: Fidelity 9.1% return per year Optima 16.1% return per year CaseWay 7.3% return per year Safeway 5.6% return per year National 12.3% return per year Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.Formulate the LP model for this problem, using the standard LP format. Remember to define the objective function, the decision variables, and label the constraint functions. There is no need to solve the problem. Note:- Do not provide handwritten solution. Maintain…
Over the next three years, the expected path of 1-year interest rates is 4, 1, and 1 percent, and the 1-yaer, 2-year, and 3-year term premia are 0, 1, and 2 percent, respectively. The liquidity premium theory of the term structure predicts that the yield curve Question 4 options: slopes upward. has a ^ shape. slopes downward. has a V shape.
George Johnson recently inherited a large sum of money;he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6 percent for the bond fund and 10 percent for the stock fund.Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest atleast 30 percent of that amount in the bond fund. In addition he wants to select a mix that will enable him to obtain a total return of atleast 7.5 percent. A) Formulate a linear programming model that can be used to determaine the percentage that should be allocated to each of the possible i nvestment alternatives B) Solve the problem using the graphical solution procedure.