xplain the term “Constrained Optimization” as Thaler used in the first chapter of Misbehaving.
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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%.Discuss a situation where constrained optimization is used?Why Modifying the objective function is required?
- Which of the following are the four fundamental assumptions of resilient optimization?'Answer the 3 subparts in 2 sentences each. For each of the following scenarios, please identify the most appropriate Operations Research model. RPI is facilitating a mentorship program and wants to assign undergraduate students with graduate student mentors. There are more undergraduate students than graduate students; therefore, each graduate student can be assigned at most 3 undergraduate student mentees. The goal is to maximize assignment satisfaction. The children’s game Snakes and Ladders is played in a sequential fashion. If a player is on a given square, the player can move to a different square based on selecting a card. This is a game of chance and there is no strategy in the game. The goal is predict who will win the game given the current location of both players. The US government wants to connect all major US cities with high-speed internet lines, which requires laying lines below ground. The US government wants to use the least amount of high-speed lines to connect…Answer the 3 subparts in 2 sentences each. For each of the following scenarios, please identify the most appropriate Operations Research model. RPI is facilitating a mentorship program and wants to assign undergraduate students with graduate student mentors. There are more undergraduate students than graduate students; therefore, each graduate student can be assigned at most 3 undergraduate student mentees. The goal is to maximize assignment satisfaction. The children’s game Snakes and Ladders is played in a sequential fashion. If a player is on a given square, the player can move to a different square based on selecting a card. This is a game of chance and there is no strategy in the game. The goal is predict who will win the game given the current location of both players. The US government wants to connect all major US cities with high-speed internet lines, which requires laying lines below ground. The US government wants to use the least amount of high-speed lines to connect…
- 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.What are some common properties of LP models? What is the three-step process for solving LP models? How are constraints modeled graphically? What is the corner point property? How is it useful in solving LP models?What is meant by the term "dynamic programming"?
- Describe what is meant by the assumption of linear programming?Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file. An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Return Maximum Allowed Low-income mortgage loans 6.50% 20% Conventional mortgage loans 6.00% 30% Government sponsored mortgage loans 8.25% 25% Bond investments 5.75% 15% Stock investments 8.75% 18% Futures trading 9.25% 10%Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,300, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $16 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week s4 = 1 if the production line is set up to…