Suppose that you are interested in choosing a set of investments {1,...,7} using 0 - 1 variables. Model the following constraints using only linear equations (obs: operators such as or or if can not be used): (a) You cannot invest in all of them. (b) You must choose at least one of them. (c) Investment 1 cannot be chosen if investment 3 is chosen. (d) Investment 4 can be chosen only if investment 2 is also chosen. (e) (bonus) You must choose either both investments 1 and 5 or neither. (f) (bonus) You must choose either at least one of the investments 1,2,3, or at least two investments from 2.4.5.6.

Suppose that you are interested in choosing a set of investments {1,...,7} using 0 - 1 variables. Model the following constraints using only linear equations (obs: operators such as or or if can not be used): (a) You cannot invest in all of them. (b) You must choose at least one of them. (c) Investment 1 cannot be chosen if investment 3 is chosen. (d) Investment 4 can be chosen only if investment 2 is also chosen. (e) (bonus) You must choose either both investments 1 and 5 or neither. (f) (bonus) You must choose either at least one of the investments 1,2,3, or at least two investments from 2.4.5.6.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

See similar textbooks

Similar questions

Suppose you have a linear optimization model where you are trying to decide which products to produceto maximize profit. Answer the following questions and be as specific as possible.(a) What does the additive assumption imply about the profit objective? (b) What does the proportionality assumption imply about the profit objective? (c) Can you think of any reasonable profit functions that would not be linear in the amounts of theproducts produced?
Eng. Economic Q1. Would a dollar tomorrow be worth more to you today when interested is 20% or 10%?
Need help on part (d) and (e) 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply decreases.…
In the formula ke >= (D1/P0) + g, what does (D1/P0) represent?
A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $
Help me to determine the answer and follow the direction.Thank you!
Which of the different graphs studied would be most appropriate for the following? a. The percentage composition of the monthly budget of P55, 000 for a family of six. b. To show the annual changes in the student population of a certain university during a 10-year period beginning 1997. c. A comparison of the size of student population for 5 different universities in Metro Manila. d. Show the trend in the monthly sales of a large department store over a period of one year. e. Showing the relationship, if there is any, between poverty and criminality.
Exercise 3. Your software company recently instituted a highly regarded training program for newly hired software developers. The benefits of this program include not only the benefits to employees, but also the goodwill generated by an increase in your reputation among customers and professional groups. The costs of this training program include all of the labor, space, and consultants necessary. Suppose these benefits and costs are given by B(Q) = 100Q2Q² and C(Q) = 100, where Q represents the amount of hours each software developer should spend in training. (Note that MB = 100 – 4Q, MC = 10, and also that time can be measured in fractions of one hour.) a. What level of Q maximizes the total benefits of your newly introduced training pro- gram? b. What level of Q minimizes the total costs of the program? c. What level of Q maximizes the net benefits? d. What level of training is optimal? Why?
Methods or techniques applied in maximizing of minimizing an objective function. * decision science tools mathematical economics optimization techniques econometrics
Suppose that sales revenue (S) depends upon the quantity of advertising (A), in a relationship estimated as: S= 14 + 16A-2A2 Task: how many unit of advertising should be undertaken to maximize sales?
I need some help and can you show me all the steps, please The profit of a firm is described by the following function: f(Q) = -8Q^3 + 30Q^2 – 120Q – 100 where Q is the quantity produced. (A) Find the stationary points for this function. (B) Using the first derivative test, find for what value of Q the profit maximised. (C) Find the feasible values of Q where the graph of the profit function is concave up.
I need the answer as soon as possible