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- 2) A farmer is planning the crops that will be planted in the upcoming season. The farmer can get $353.08 per metric ton of soybean, $119.42 per metric ton of barley, $163.80 per metric ton of corn, and $212.64 per metric ton of wheat. The total capacity of the farm is 400 metric tons of product. Based on rising tariffs, at most, the soybeans should constitute 20% of the total crop. Prices for barley and wheat have been declining, so corn should at least be 175 metric tons. a. Solve the linear program using Solver and write the strategy. b. Run a sensitivity analysis and identify the constraints that are binding. c. What is the change in the objective function value if the minimum for corn was 100 metric tons and the farmer acquired land that could produce 75 more metric tons of crop? Please show work in excel2. As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs $10,000 and each training program on problem solving costs $8000. a. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem solving that should be offered in order to minimize total cost. b. Determine the optimal…Let x = pieces of sofa, Y=pieces of table, Z=pieces of chair1.What is the objective function?2. Express the first constraint (wood) in mathematical sentence3. Express the second constraint (upholstery) in mathemathical sentence.4. Express the third constraint (Labor) in mathemathical sentence
- JANE’S SWEET STUFF BAKERYJane Brown has operated Jane’s Sweet Stuff Bakery for the past 6 years. By 5:00 a.m. everyweekday morning, customers are dropping in both to enjoy the cozy smells and to purchasefresh warm donuts and other goodies to enjoy with their coffee before going to work. After 5years of this schedule where she began baking by 3:00 a.m., Jane is very tired.Jane has decided to hire an apprentice baker and a cashier to provide early morning counterhelp. She knows that she must stop treating her bakery as an extension of herself and beginoperating a business. She has a friend with an MBA who told her to establish a performancemeasurement system, so that she can tell whether her two new employees are goodemployees or not.It all seems so complicated. Jane has contacted the local Business School Co-op Program andasked for advice. Your professor assigned you to answer Jane’s questions for 20 percent of yourgrade. When you meet with Jane, she tells you that she will need you to…Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?1. The following diagram represents a flow network. Each edge is labeled with its capacity, the maximum amount of stuff that it can carry. a. Formulate an algebraic model for this problem as a maximum flow problem. b. Develop a spreadsheet model and solve this problem. What is the optimal flow plan for this network? What is the optimal flow through the network?
- Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its Des Moines factory and to cut back the production capacities at its other two factories. It also recognizes a shifting market for its desks and revises the requirements at its three warehouses. The table on this page provides the requirement at each of the warehouses, the capacity at each of the factories, and the shipping cost per unit to ship from each factory to each warehouse. Find the least-cost way to meet the requirements given the capacity at each factory.Baton Rouge's Mt. Cedar Hospital is a large, private, 600-bed facility complete with laboratories, operating rooms, and X-ray equipment. In seeking to increase revenues, Mt. Cedar's administration has decided to make a 90-bed addition on a portion of adjacent land currently used for staff parking. The administrators feel that the labs, operating rooms, and X-ray department are not being fully utilized at present and do not need to be expanded to handle additional patients. The addition of 90 beds, however, involves deciding how many beds should be allocated to the medical staff (for medical patients) and how many to the surgical staff (for surgical patients). The hospital's accounting and medical records departments have provided the following pertinent information. The average hospital stay for a medical patient is 8 days, and the average medical patient generates $2,280in revenues. The average surgical patient is in the hospital 5 days and generates $1,515 in…
- Formulate but do not solve the problem.The management of Hartman Rent-A-Car has allocated $2.25 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $18,000 each, intermediate-size cars cost $27,000 each, and full-size cars cost $36,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.) = 2,250,000 = x = 100A chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, andchocolates.A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a…Answer the following questions after reviewing the problem. 4. Problem 5.17: American Football. The offensive coordinator for the Chicago Bears professional football team is preparing a game plan for the upcoming game against the Green Bay Packers. A review of game tapes from previous Bears–Packers games provides data on the yardage gained for run plays and pass plays. Data shows that when the Bears run against the Packers’ run defense, the Bears gain an average of 2 yards. However, when the Bears run against the Packers’ pass defense, the Bears gain an average of 6 yards. A similar analysis of pass plays reveals that if the Bears pass against the Packers’ run defense, the Bears gain an average of 11 yards. However, if the Bears pass against the Packers’ pass defense, the Bears average a loss of 1 yard. This loss, or negative gain of −1, includes the lost yardage due to quarterback sacks and interceptions. Develop a payoff table that shows the Bears’ average yardage gain for each…
