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.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 68P

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Fopic 4- Linear Programming: Appli eBook Problem 9-05 (Algorithmic) Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 ounces of hot sauce. Today, Kilgore has 21 pounds of beef, 16 cups of onions, 89 ounces of Kilgore's special sauce, and 61 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today.…
4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?
11
4. Optimal Rental Decisions in Cloud Computing Assume that AWS has the following 3 options for renting servers. Fraction of Job in one Server Description Rental Low Power Medium Power High Power $2/hr. $4/hr. $9/hr. Hour 1/8 1/6 1/3 L M Note that if you rent a server for less than one hour, you still must pay the rent for the entire hour. You have a job that must finısh in at most 5 hours. The low-power server can finish 1/8th of the job in 1 hour, the medium-power server can finish 1/6 of the job in one hour, and the high- power server can finish 1/3rd of the job in one hour. (a) The typical practice used by most firms is to find a single server that can do the work at the least cost and within the available time. Find the best sıngle server solution-that is, which single server should you use and for how many hours will you rent this server?
Let’s consider the following LP problem: min Subject to: Solve the problem with the graphic method.
Scenario You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram below:
Please solve this Optimization problem
Please answer correctly write by hand please
Bill builds benches in a small shop and he plans to operate five 8-hour days perweek. Each bench has two ends and a top. It takes 5 minutes to cut and sand eachend and 2 minutes to make each top. Assembly requires 8 minutes per bench, andpainting requires 5 minutes per bench. Bill has one employee who makes the topsand ends. Bill will do the final assembly and painting. He also plans 1 hour per dayfor setup and teardown for each department.a. How many benches should he plan to build per week?b. How many hours per week are required for each person?c. Suggest ways to increase the number of benches produced per week
Green Vehicle Inc. manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/60 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/50 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicle sold. a) Define the objective function and constraint equations. b) Graph the feasible region. c) What is a maximum-profit daily production plan at the new factory? d) How much profit will such a plan yield, assuming whatever is produced is sold?
2. Solve the LP using isocost method. Min Z = 2x + y s.t. x + y ≥5 2x + 6y ≥ 18 3x - y ≥ 3 x-2y ≤4 x, y ≥ 0
A network of railway lines connects the main lines entering and leaving a city. Speed limits, track reconstruction, and train length restrictions lead to the flow diagram below, where the numbers represent how many cars can pass per hour. Max s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7 Flows Node 8 Flows Node 9 Flows Node F Flows Max Flow on Arcs 500 all x > 0 for all i and j. 300 5 600 300 400 400 3 150 6 200 300 Formulate an LP to find the maximal flow in cars per hour from node 1 to node 10. (Let x, represent the flow from node i to node j. Enter your maximum flows as a comma-separated list of inequalities.) Kij 7 200 500 400 350 8 300 600 300 9 450 500 10

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