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- Formulate the following as a linear programmingproblem: A greenhouse operator plans to bid for the job ofproviding flowers for city parks. He will use tulips, daffodils,and flowering shrubs in three types of layouts. A Type 1layout uses 30 tulips, 20 daffodils, and 4 flowering shrubs.A Type 2 layout uses 10 tulips, 40 daffodils, and 3 floweringshrubs. A Type 3 layout uses 20 tulips, 50 daffodils, and 2flowering shrubs. The net profit is $50 for each Type 1layout, $30 for each Type 2 layout, and $60 for each Type 3layout. He has 1,000 tulips, 800 daffodils, and 100 floweringshrubs. How many layouts of each type should be used toyield maximum profit?Formulate the following as a linear programmingproblem: A greenhouse operator plans to bid for the job ofproviding flowers for city parks. He will use tulips, daffodils,and flowering shrubs in three types of layouts. A Type 1layout uses 30 tulips, 20 daffodils, and 4 flowering shrubs.A Type 2 layout uses 10 tulips, 40 daffodils, and 3 floweringshrubs. A Type 3 layout uses 20 tulips, 50 daffodils, and 2flowering shrubs. The net profit is $50 for each Type 1layout, $30 for each Type 2 layout, and $60 for each Type 3layout. He has 1,000 tulips, 800 daffodils, and 100 floweringshrubs. How many layouts of each type should be used toyield maximum profit?36 Explain how your formulation in Problem 35 changesif both of the following conditions are added:a The number of Type 1 layouts cannot exceed thenumber of Type 2 layouts.b There must be at least five layouts of each type.Assign nine automobile service departments to bays in a 3 × 3 grid so that the closeness ratings Problem 2 in the following matrix are satisfied. (The unimportant and ordinary-importance ratings have been omitted to simplify the example.) The location of department 4 must be in the upper right-hand corner of the grid to satisfy a town ordinance.
- 9-43. Northwest University is in the process of complet-ing a computer bus network that will connect com-puter facilities throughout the university. The prime objective is to string a main cable from one endof the campus to the other (nodes 1–25) throughunderground conduits. These conduits are shownin the network below; the distance between them isin hundreds of feet. Fortunately, these undergroundconduits have remaining capacity through which thebus cable can be placed.(a) Given the network for this problem, how long (inhundreds of feet) is the shortest route from node1 to node 25?(b) In addition to the computer bus network, a newphone system is also being planned. The phonesystem would use the same underground conduits. If the phone system were installed, the follow-ing paths along the conduit would be at capacity and would not be available for the computer busnetwork: 6–11, 7–12, and 17–20. What changes(if any) would you have to make to the pathused for the computer bus if the phone…Assign the 4 departments in Table X to locations A, B, C, and D, which are separated by the distances shown in Table y, in such a way that transportation cost is minimized. Use this heuristic: assign departments with the greatest interdepartmental workflow first. (See attached table) Illustrate the configuration of the 4 departments in each of the 4 locations. Show the distances between departments and total interdepartmental workflows of department pairs.Avis Company is a car rental company that is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 2 minutes. The average traveling time (round-trip) is 20 minutes.a. How many Avis buses are traveling to and from the airport?b. The branch manager wants to improve the service and suggests dispatching buses every 0.5 minutes. She argues that this will reduce the average traveling time from the airport to the Avis offices to 2.5 minutes. Is she correct? If your answer is negative, what will the average traveling time be?
- Johnson Cogs wants to set up a line to serve 60 customers perhour. The work elements and their precedence relationshipsare shown in the following table.a. What is the theoretical minimum number of stations?b. How many stations are required using the longest workelement decision rule?c. Suppose that a solution requiring five stations is obtained.What is its efficiency?James Lawson’s Bed and Breakfast, in a small his-toric Mississippi town, must decide how to subdivide (remodel) the large old home that will become its inn. There are threealternatives: Option A would modernize all baths and combinerooms, leaving the inn with four suites, each suitable for two tofour adults. Option B would modernize only the second floor; theresults would be six suites, four for two to four adults, two fortwo adults only. Option C (the status quo option) leaves all wallsintact. In this case, there are eight rooms available, but only twoare suitable for four adults, and four rooms will not have privatebaths. Below are the details of profit and demand patterns thatwill accompany each option: ANNUAL PROFIT UNDERVARIOUS DEMAND PATTERNSALTERNATIVES HIGH P AVERAGE PA (modernize all) $90,000 .5 $25,000 .5B (modernize 2nd) $80,000 .4 $70,000 .6C (status quo) $60,000 .3 $55,000 .7Which option has the highest expected monetary value?A recruiter for a job placement agency is considering whether to pay $50,000 per year to lease a new recruiting facility in a prime location in Washington D. C. He estimates it will cost $50 per recruit to process the paperwork at this new location. He receives a $75 commission for each new recruit he processes. Part A - If the office space at this new location has design and effective capacities of 10,000 and 8,000 recruits processed annually, respectively, and 6,000 recruits will be processed per year, what will be the utilization of the office space?Part B - If his office space at this new location has design and effective capacities of 10,000 and 8,000 recruits processed annually, respectively, and he plans to be 90% efficient in his use of this space, how many recruits does he plan to process per year?
- You must tight any constraints from your own and. Graph it and aolve a and bProblem 1, see picture Please information for C is different from the one solution found online : A workshop has three (3) types of machines A, B, and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C. The following table shows The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit soldMaximal Flow a. Write the linear program for this problem. b. Create a spreadsheet model to find the maximal flow from node 1 to 6