11:18 AM...0.1KB/s ©80Chapter 6 The Transportaiton problem - Read-onlyRead Only - You can't save changes to this file.Save a copyDismissExerciseA model formulation exercise of Transportation Problem6.1. The Childfair Company has three plants producing child push chairs that are to be shipped to fourdistribution centers.Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs toreceive 10 shipments per month. The distance from each plant to the respective distributing centers is given inthe table.DistanceDistribution Center23700 miles800 miles 1,300 miles1,100 miles 1,400 miles600 miles 1,200 miles400 miles1,000 miles900 milesPlant600 miles3800 milesThe freight cost for each shipment is $100 per mile.How much should be shipped from each plant to each of the distribution centers to minimize the totalshipping cost?(a) Draw the network representation of this problem.(b) Construct the appropriate parameter table and formulate this problem as a transportation problem.III

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 67P

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Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????
The number of crimes in each of a city’s three policeprecincts depends on the number of patrol cars assigned toeach precinct (see Table 11). Five patrol cars are available.Use dynamic programming to determine how many patrolcars should be assigned to each precinct. No. of Patrol Cars Assigned to PrecinctPrecinct 0 1 2 3 4 51 14 10 7 4 1 02 25 19 16 14 12 113 20 14 11 8 6 5
Which of the following could not be a constraint for a linear programming problem? Multiple Choice 1A + 2B = 3 1A + 2B 1A + 2B ≤ 3 1A + 2B ≥ 3 1A + 2B + 3C ≤ 3
J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. Atthe beginning of January, Huggys has a 30% market7.9 Conclusion 401share. During any month, 10% of the people whopurchase Huggys defect to brand X, and a fraction0.2a1y2 of customers who usually buy brand X switchto Huggys, where a is the amount spent on advertisingin millions of dollars. For example, if you spend $4million during a month, 40% of brand X’s customersswitch to Huggys. Your goal is to maximize J&J’saverage market share during the next 12 months,where the average is computed from each month’sending share. Determine an appropriate advertisingpolicy. (Hint: Make sure you enter a nonzero trialvalue for each month’s advertising expense or Solvermight give you an error message.)
A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.
We have 60 meters of fence and want to fence a triangular shaped area. Please formulate an NLP (do not try to solve) that will enable us to maximize the fenced area (Hint: The area of a triangle with sides of length a, b, and c is ( s (s – a) (s – b) (s – c))1/2, where s is half the parameter of the triangle).
Suppose an assignment problem, where there are 3 employees who must perform 3 different tasks. The times (in hours) that employees take to perform each of the tasks is shown below. Each employee must perform only one task, and a task can only be performed by one employee. All employees are paid exactly the same wage per hour of work. Minimize the total time to make all tasks. Task 1 Task 2 Task 3 Employee 1 154 29 40 Employee 2 18 137 12 Employee 3 94 13 31 How many variables does the problem have? How many constraints does the problem have? The objective function corresponds to:
hapter 7. Crypt-Me-Not Investments, Inc. is a new investment firm that deals exclusively with cryptocurrency investments. An investor wants to invest $75,000 in cryptocurrency next year and approaches them about investing in Solana (SOL), Dogecoin (DOGE), and Bitcoin (BTC) which are currently selling at $175, $1.00, and $26,000 per unit respectively. The expected annual return on each unit of SOL is $250, on each unit of DOGE is $100, and on each unit of BTC if $22,000. Like everyone else, the investor wants to maximize the returns on the investment. The risk index associated with each unit of SOL is 1.6, with each unit of DOGE is 1.8, and with each unit of BTC is 1.1. Crypt-Me-Not recommends not crossing a total risk value of 2500 with their clients investments. Moreover, BTC is the dominant crypto currency, so the investor insists that a minimum of 1 unit of BTC is necessary for the portfolio. Based on these constraints, formulate a Linear Program, and answer the following questions…
Calvin Butterball is chief of operations for the Fly-by-Night Aircraft Corp. He is responsible for the manufacturing of the company's two models of planes: The parrot and the eagle. Each department of the company has restrictions concerning the number of planes, which can be manufactures each day. No more than 7 eagles and no more than 11 parrots can be manufactured per day. No more than 12 total planes total can be shipped per day. The number of eagles manufactures must be no more than twice the number of parrots manufactured each day. You much use more than 1000 hours of labor per day; it takes 100 man-hours to manufacture each parrot and 200 man-hours to manufacture each eagle. Fly-by-Night makes a profit of $300 per parrot and $200 per eagle. How many eagles and how many parrots should e produced per day to give the greatest feasible profit and to determine the profit?
57. A beer company has divided Bloomington intotwo territories. If the company spends x1 dollarson promotion in territory 1, it can sell 60x11y2 casesof beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x21y2 cases of beerthere. Each case of beer sold in territory 1 sells for$10 and incurs $5 in shipping and production costs.Each case of beer sold in territory 2 sells for $9 andincurs $4 in shipping and production costs. A total of$5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, byapproximately how much would the company’sprofit increase? By how much would its revenueincrease?c. Use SolverTable to see how a change in the priceof beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.
Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15 2x1 +x2 + 5x3 = 20 x1 +2x2 +x3 +x4 = 10 x1 + 4x2 +6x3 ≤ 5 Where x x x x1, 2, 3, 4 ≥ 0
Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on 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 $1,500 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 $2,500 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 $3,000 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 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…

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