2The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certainbuildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that eachbuilding is cleaned. The management science department formulated the following linear programming model to help with theselection process.Min 250x1 + 260x2+ 240x3+ 300x4 + 230x5 + 270x6 + 280x7 + 250xgs.t. x1 + x2 + x5 + x7 2 1{Building A constraint}X1 + X2 + x3 1{Building B constraint)X6 + xg Z 1{Building C constraint)X1 + X4 + x7 2 1{Building D constraint)x2 + x7 Z 1{Building E constraint)X3 + Xg 2 1{Building F constraint)> 1 (Building G constraint)X1 + X4 + x6 2 1 (Building H constraint)X1 + X4 + Xg 2 1 (Building I constraint}X1 + X2 + x7 1{Building J constraint)X2 + X5 + X7| 1, if crew j is selected"j-l0, otherwiseSet up the problem in Excel and find the optimal solution.a. What is the cost of the optimal crew assignment?Cost of optimal crew assignment Set up the problem in Excel and find the optimal solution.a. What is the cost of the optimal crew assignment?Cost of optimal crew assignmentb. Which crews are assigned to work?Crew 1 willCrew 2 willCrew 3 willCrew 4 willCrew 5 willCrew 6 willCrew 7 willCrew 8 will

Objective Functions and Constraints: Based on the given details, the objective…

Answered: The university is scheduling cleaning…

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 86P

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Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
What is Optimization? How many methods are there to calculate it? Explain this? 2- What do we mean by function Objective? What do we mean by constraints? 3- Give three practical examples (physical or engineering) of a target function with a constraint
Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
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Suppose Jack like to solve the following formulation in Excel. And the problem is setup in Excel like this: See attached picture. A B C D E 1 X1 X2 2 decision variable objective 3 coefficient of objective function 2 3 4 Constraints LHS RHS 5 Constraints 1 2 1 3 6 Constraints 2 4 5 20 7 Constraints 3 2 8 16 8 Constraints 4 5 6 60 We want to put our objective function in cell D3. What should we type in D3? In cell D5 to D8, we will put the left hand side of our constraint. What should we type in D8? In OpenSolver, what should we assign to Variable Cell? What should you do to input the non-negativity constraint in OpenSolver?
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Instruction: Formulate the dual problems for X2 the following linear programming model No need to compute/doing a tableau 1. Maximize Z = 2X1 + X2 Subject to: X2 < 10 2X1 + 5X2 < 60 X1 + X2 <18 3X1 + X2 < 44 2. Maximize Z = 2X1 + X2 +3X3 Subject X1 + X2 + 2X3 < 400 2X1 + X2 + X3 < 500 3. Maximize Z = 80X1 + 60X2 Subject X1 + X2 = 200 X1 < 50 X2 > 80
A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network. The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively. The models require the labor and materials per unit shown below. Portable Student Office Network Total Labor (hrs/week) 5 5 6 8 4000 Chassis (unit/week) 1 1 1 1 400 Disk Drive (unit/week) 2 1 2 1 300 Hard Disk (unit/week) 0 0 0 1 20 Memory Chip (unit/week) 16 8 32 64 22,000 Circuit Bds. (unit/week) 1 1 2 4 10,000 How many of each model should be produced to maximize profit. What is the maximum profit?
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A company has a total of 3 factories to produce steel and iron. Every month, the companymust meet the following demands: 3200 tonnes of steel and 1000 tonnes of Iron. Each factoryhas a different shipping cost per tonne (£/tonne) for each product as shown in the tablebelow:Factory Steel Iron1 200 5002 800 4003 500 1000The warehouses in Factory 1, Factory 2 and Factory 3 can store 2000 tonnes,1500 tonnes and2500 tonnes of products, respectively. The company is seeking for a solution to minimise theshipping cost.a) Based on the table above, determine the optimal monthly assignment plan for the factory.That is, how many tonnes each factory needs to be shipped to fulfil the demand.b) Suppose Factory 3 will not be available during the next few months. Keeping the samedemand, is the company able to fulfil the demands? What would be the revised assignmentplan to ensure demand is fulfilled?c) The cost of raw materials in each factory is shown in the table below. Change the companyobjective…

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