find the a. decision variablesb. objective function c. constraints )A certain analyst wants to solve a problem about a company that wants to minimize the total cost of transferring500 units of finished products from three different production plants to three different storage facilities, and from these threestorage facilities to three different retailers (transacts with the customers). Each of the production plants, storage facilities,and retailers have different capacities, which are shown in the following table.Transfer PointsProduction PlantStorage FacilityRetailer1100 units330 units350 unitsProduction PlantStorage facilityCapacities2150 units240 units100 unitsThe transportation cost per unit (in $) from the three production plants to the three storage facilities are shown below.Storage facility123N1 2 31302 203 8050312888 N80250 units230 units50 unitsThe transportation cost per unit (in $) from the three storage facilities to the three retailers are shown below.Retaller90 304040702010Help the analyst solve the problem by formulating the Linear Programming Model of the problem.370

Transshipment is a special case of transportation problem of linear program. In such problems there…

Answered: find the a. decision variables b.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 67P

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Solve the following Linear programming problem using the simplex method:Maximize Z = 10X1 + 15X2 + 20X3subject to:2X1 + 4X2 + 6X3 ≤ 243X1 + 9X2 + 6X3 ≤ 30X1, X2 and X3 ≥ 0(b) Suppose X1, X2, X3 in (a) refer to number of red, blue, and green balloons respectivelywhich are produced by a company per day. And Z is the total profit obtained afterselling these balloons. Interpret your answer obtained in (a) above(c) Write the dual of the following linear programming problem:Minimize Z = 2X1 − 3X2 + 4X3subject to:3X1 + 4X2 + 5X3 ≥ 96X1 + X2 + 3X3 ≥ 47X1 − 2X2 − X3 ≤ 105x1 − 2X2 + X3 ≥ 34X1 + 6X2 − 2X3 ≥ 3X1, X2 and X3 ≥ 0
Consider the following puzzle. You are to pick out 4three-letter “words” from the following list:DBA DEG ADI FFD GHI BCD FDF BAIFor each word, you earn a score equal to the position thatthe word’s third letter appears in the alphabet. For example,DBA earns a score of 1, DEG earns a score of 7, and so on.Your goal is to choose the four words that maximize yourtotal score, subject to the following constraint: The sum ofthe positions in the alphabet for the first letter of each wordchosen must be at least as large as the sum of the positionsin the alphabet for the second letter of each word chosen.Formulate an IP to solve this problem.
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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.
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A company has 30,000 employees in three cities as shown in the table below. It wishes to give promotions to 200 employees. Cities A B C Total Original Number of Employees 9140 6070 14,790 30,000 a) Apportion the promotions using Hamilton's method. b) Suppose that in 10 years the cities have the following number of employees and the company wishes to again give promotions to 200 employees. Does the population paradox occur using Hamilton's method? Cities A B C Total Number of Employees 10 years later 9190 6070 14,890 30,150 a) Complete the table with Hamilton's apportionment for the original number of employees. Cities A B C Total Original Number of Employees 9140 6070 14,790 30,000 Hamilton's Apportionment ? ? ? 200
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…
A company that sells computer network systems is planning to offer free memory storage services to its customers where picture, music, and video files can be stored. The company is planning to initially start with three servers, each of whose capacity is provided in Table 2. The company anticipates that its customers may store up to 300,000 picture files, up to 100,000 music files, and up to 100,000 video files. A typical picture file is expected to be accessed 8,000 times a year, whereas each music and each video file are expected to be accessed 4,000 and 2,000 times per year, respectively. Whenever a customer accesses a file, it will have to be retrieved to become available again. The amount of time that it takes for a file to be retrieved depends on the type and the server being used (Table 3). Write a programming model that minimizes the total annual time that users spend accessing their files.
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For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.
The standard form of the following linear programming model is given. Find the values of variables at the point of intersection of constraint 1 and the vertical axis (y). (Round your answers to 3 decimal places.) Maximize P = 30x + 15y + 0s1 + 0s2 subject to 6x + 12y + s1 = 19 13x + 12y + s2 = 35 and x, y, s1, s2≥ 0.

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find the a. decision variables b. objective function c. constraints