Please no written by hand solution Problem 3:Consider a restaurant that is open seven days a week. Based on past experience, the number of workersneeded on a particular day is given as follows:dayTueWednumber1315Mon14Thur16Fri19Sat18Every worker works five consecutive days, and then takes two days off, repeating this patternindefinitely. How can we minimize the number of workers that staff the restaurant?Please specify the decision variables, the objective function and the constraints.Sun11

Linear Programming is a mathematical and statistical tool that is used in operations management to…

Answered: Problem 3: Consider a restaurant that…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 80P

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. Solve each of these problems by computer and obtain the optimal values of the decision variablesand the objective function.a. Maximize Z = 4x1 + 2x2 + 5x3Subject to1x1 + 2x2 + 1x3 ≤ 251x1 + 4x2 + 2x3 ≤ 40 3x1 + 3x2 + 1x3 ≤ 30x1, x2, x3 ≥ 0 b. Maximize Z = 10x1 + 6x2 + 3x3Subject to1x1 + 1x2 + 2x3 ≤ 252x1 + 1x2 + 4x3 ≤ 40 1x1 + 2x2 + 3x3 ≤ 40x1, x2, x3 ≥ 0
Problem There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $1000 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $2000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 ton. The state wants to reduce the amount of P 1in the river by at least 30 tons and the amount of P2 by at least 40 tons. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what…
PROBLEM 6 An investment firm has $1 million to invest in stocks, bonds, certificates of deposit, and real estate. The firm wishes to determine the mix of investments that will maximize the cash value at the end of 6 years. Opportunities to invest in stocks and bonds will be available at the beginning of each of the next 6 years. Each dollar invested in stocks will return $1.20 (a profit of $0.20) 2 years later; the return can be immediately reinvested in any alternative. Each dollar invested in bonds will return $1.40 3 years later; the return can be reinvested immediately. Opportunities to invest in certificates of deposit will be available only once, at the beginning of the second year. Each dollar invested in certificates will return $1.80 four years later. Opportunities to invest in real estate will be available at the beginning of the fifth and sixth years. Each dollar invested will return $1.10 one year later. To minimize risk, the firm has decided to diversify its…
Problem: A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 150 hours, and the tiller is available for 200 hours. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. How many acres of each crop should be planted to maximize the farmer’s profit? (Let W be the number of acres of wheat to be planted, B the number of acres of barley to be planted and P the profit) (a) What is the objective function for the problem? (b) Excluding the non-negative constraint, how many constraints does the problem have? (c) What is the linear programming model of the problem?
Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem. You may use Excel to solve the mathematical problems. 1. Sunchem, a manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table 1 along with the cost of producing 1 ton of ink at each facility. The major markets for the inks are North America, Europe, Japan, South America, and the rest of Asia. Demand at each market is shown in Table 1. Transportation costs from each plant to each market in U.S. dollars are shown in Table 1. Management must come up with a production plan for the next year. a. If no plant can run below 50 percent capacity, how much should each plant produce and which markets should each plant supply? b. If there are no limits on the minimum amount produced in a plant, how much should each plant produce?
Solve each of these problems by computer and obtain the optimal values of the decision variables and the objective function. Maximize Z = 4x1 + 2x2 + 5x3 Subject to 1x1 + 2x2 + 1x3 ≤ 25 1x1 + 4x2 + 2x3 ≤ 40 3x1 + 3x2 + 1x3 ≤ 30 x1, x2, x3 ≥ 0 Maximize Z = 10x1 + 6x2 + 3x3 Subject to 1x1 + 1x2 + 2x3 ≤ 25 2x1 + 1x2 + 4x3 ≤ 40 1x1 + 2x2 + 3x3 ≤ 40 x1, x2, x3 ≥ 0
Bugs Bunny and Daffy Duck are contestants on a game show called Split or Steal. On the show, Bugs and Daffy have to pick one of two cards and decide to split the prize money of $100,000 or steal it from the other contestant. The decisions are made simultaneously so neither player knows what the other will do. The table below represents the result of the contestants’ choices. See attached What should a rational player do in this game? Is this a zero-sum game?
Al, Barbara, Carol, and Dave have joined together to purchase two season tickets to the Giants’ home football games. Because there are eight home games, each person will get tickets to two games. Each person has ranked the games they prefer from 1 to 8, with 1 being most preferred and 8 least preferred, as follows: Determine the two games each person should get tickets for that will result in the groups’ greatest degree of satisfaction. Do you think the participants will think your allocation is fair?
Formulate the problem, giving the decision variables (these must be clearly defined), objective function, and constraints. That is, give the mathematical model. (Note: you do not have to solve this linear programming problem.
In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the 11 constraints and explain A used t company, owned by Musa in Ottawa sells 7 different brands covering 3 different products. These are 4 Brands of Cars: Toyota, Honda, Chevrolet and BMW; 2 brands of Motorcycles: Suzuki and Yamaha, and 1 brand of Sailboats: Amel. Musa knows that his sales floor which he will display his products is 70,000 square feet, and that a Car takes 60 square feet of space, a motorcycle takes 20 square feet of space, and a sailboat takes 800 square feet of space. The profit that can be made for selling each of 7 different items is listed below: ITem Profit per unit Car - Toyota $2800 Car - Honda $3900 Car - Chevrolet $2,100 Car - BMW $5000 Motorcycle - Suzuki $1,000 Motorcycle - Yamaha $2,250 Sailboat - Amel $9,500 The transportation company is trying to determine how many of each item to order to maximize profit, given the following restrictions:…
PROBLEM SOLVING (DECISION THEORY) Example: A farmer wants to decide which of the three crops he should plant on his 100 Acre farm. The profit from each is dependent on the rainfall during the growing seasons. The farmer has categorized the amount of rainfall as high, medium, low. His estimated profit for each is show in the table: Rainfall Crop A Crop B Crop C High 8000 3500 5000 Medium 4500 4500 5000 Low 2000 5000 4000 Determine the various criterion from which the final decision has to be made. If the farmer wishes to plant only one crop, decide which will be his choice using the following criterion•Maximax criterion •Maximin criterion •Hurwicz criterion •Laplace criterion
A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diet must have between 1,800 and 3,600 calories. No more than 1,400 calories can be starch, and no fewer than 400 can be protein. The varied diet is to be made of two foods: A and B. Food A costs $0.75 per pound and contains 600 calories, 400 of which are protein and 200 starch. No more than two pounds of food A can be used per resident. Food B costs $0.15 per pound and contains 900 calories, of which 700 are starch, 100 are protein, and 100 are fat. (Answers in Appendix D)a. Write the equations representing this information.b. Solve the problem graphically for the amounts of each food that should be used.

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