Explanation of Solution
Formulation of a Linear
From the given information, let consider “x1” bet the amount of money invested in bond 1, “x2” bet the amount of money invested in bond 2, “x3” bet the amount of money invested in bond 3, “x4” bet the amount of money invested in bond 4.
The objective is to maximize the expected return on its investments.
Therefore, the objective function is,
Maximize
Constraint 1:
At least, 8% must be the worst-case return of the bond portfolio.
Constraint 2:
At most, the average duration of the bond portfolio must be 6
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Chapter 3 Solutions
Introduction to mathematical programming
- Suppose, you are working in a company ‘X’ where your job is to calculate the profit based on their investment.If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profitof 4.5 dollar.For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% where for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. Investment will always be greater or equal to 25,000 and multiple of 100.Complete the RECURSIVE methods below that take an array of integers (investments)and an iterator (always sets to ZERO(‘0’) when the…arrow_forwardA school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:arrow_forwardA company sales manager requires a sales analysis of the two products on offer atthe end of the month. The company employs five salespeople. Input values for each salesperson are name, number, gender, and total units sold forthe month, for each product (one and two). The salary of each salesperson is strictly commission-based. Each salespersonearns a basic commission calculated as 12.5% of his/her total sales. If a salesperson sells more than R1 000 of product two, he or she receives anadditional 10% commission on product two. If not, commission for sales of producttwo is reduced to 5% (i.e. instead of receiving the basic 12.5% commission for salesof product two, a penalty is paid). If a saleswoman sells more than R500 of product one, she receives a bonus of R100. An added bonus of R750 is given to each salesperson whose total commission ismore than R6 000. Each employee receives a printed pay-slip showing all the employee details, grosspay, all the deductions and/or additions,…arrow_forward
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- GENERATE THE DECISION VARIABLE SOLUTION AND GENERATE AN ANSWER REPORT 2. During the winter WeeMow Lawn Service contracts with customers for cutting lawns starting in the spring. WeeMow provides service to residential and commercial customers. The service has identified 50 possible residential customers and 15 potential commercial customers it has contacted. WeeMow services a customer once every 2 weeks during the growing season. A residential lawn on average takes 1.2 hours to cut, and a commercial property requires 5 hours to cut; the service's available work time is 8 hours, 6 days per week. The profit for a residential lawn is $23, and the profit for a commercial property is $61. The service has established a weekly budget of $350 for management, gas, and other materials, plus equipment repair. A residential lawn averages $12 in management, gas, material, and repair costs, and a commercial property averages $20 in costs. WeeMow wants to know how many residential and commercial jobs…arrow_forwardThe Frequentist approach says that given 10 coin flips you should get exactly 5 heads and 5 tails. Question 15 options: True False The Frequentist approach says that, in the long run, if we flip a coin a large number of times, we would expect an approximate 50-50 split of heads and tails. Question 16 options: True False Consider multiple trials of flipping a fair coin. As the number of trials decreases, the closer we get to an equal split of heads and tails. Question 17 options: True False The following would represent probability from the Frequentist approach: After rolling a six-sided die 300 times, we would expect to roll a 2 or a 3 about 33% of the time. Question 18 options: True Falsearrow_forwardA store purchased x packages of AAA batteries at $5 per package and y packages of AA batteries at $7 per package for a total cost of $135. If at least one package of each type of battery was purchased, what are the possibilities of the number of packages of AAA batteries and the number of packages of AA batteries?arrow_forward
- In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.arrow_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…arrow_forwardIt has been observed by management that some faculty member at the university demonstrates a lackadaisical attitude toward work. They seldom go to class yet at the end of each month they receive full salary. Management has decided that GHs 200, 300, 400, and 500 will be deducted from a faculty’s salary if he/she offends once, twice, third time and forth time respectively in a month. This means that if a faculty member offends once in a month GHs 200 will be deducted, if a faculty member offends twice in a month, GHs 500 (i.e. 200+300) will be deducted, if a faculty member offends three times in a month GHs 900 (i.e. 200+300+400), will be deducted and if a faculty member offends four times in a month GHs 1,400 (i.e. 200+300+400+500). Assuming all faculty members are on a flat salary rate of GHs 2500.a. Write a program to request for the names of four faculty members and number times he/she has absented him/herself from class. One of them should have absented him/herself once, another…arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole