Iron Works, Inc. manufactures two products made from steel and receives 2000 pounds of steel each month. It takes 2 pounds steel to make a unit of product 1, and it takes 3 pounds of steel to make a unit of product 2. The unit profits for product 1 and product 2 are $100 and $200, respectively. Each month the manufacturer has a contract calling for at least 60 units of product 1. At most 720 units of product 2 may be produced by the firm's facilities. Using the steps for optimization modeling based on chapter 4 of the data smart text, find the monthly production quantities of product 1 and product 2 to maximize profit from these products. Submit your solution as an excel file.
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- How much influence can the employee requirements for one, two, or three days have on the weekly schedule in the employee scheduling example? Explore this in the following questions: a. Let Monday’s requirements change from 17 to 25 in increments of 1. UseSolverTable to see how the total number of employees changes.b. Suppose the Monday and Tuesday requirements can each, independently of one another, increase from 1 to 8 in increments of 1. Use a two-way SolverTable to see how the total number of -employees changes.c. Suppose the Monday, Tuesday, and Wednesday -requirements each increase by the same amount, where this increase can be from 1 to 8 in -increments of 1. Use a one-way SolverTable to -investigate how the total number of employees changes.What is true about the assignment problem if the solution has reached the table below? Project A Project B Project C Project D Expert W 0 100 200 0 Expert X 0 0 200 300 Expert Y 0 100 300 0 Expert Z 200 100 0 0 a. The minimum number of vertical and horizontal lines needed to cross out 0s is three. b. Optimal assignment of projects cannot be determined yet. c. Optimal assignment of projects can now be determined.Business Analytics department chair will be scheduling faculty to teach courses during thecoming fall semester. Four core courses need to be covered. The four courses are at theUG, MBA, MS, and Ph.D. levels. Four professors will be assigned to the courses, witheach professor receiving one of the courses. Student evaluations of professors are availablefrom previous semesters. Based on a rating scale of 1 to 5, the average student evaluationsfor each professor are shown in the following table. Professor C does not have a Ph.D.and cannot be assigned to teach the Ph.D. level course. If the department chair makesteaching assignments based on maximizing the student evaluation ratings over all fourcourses, what staff assignments should be made?CourseProfessor UG MBA MS Ph.D.A 4.2 4.7 4.3 4.2B 4.1 4.4 3.9 4.5C 4.6 4.1 4.2 -D 4.8 4.0 4.6 4.4a) Develop a network representation of this problem.b) Formulate a linear programming model for this problem.c) Solve the problem by using Excel Solver…
- A) What is the theoretical minimum number of workstations? a. 3 workstations b. 3.5 workstations c. 3.83 workstations d. 4 workstations e. 5 workstations B) Which of the following statements is FALSE? a. Tasks A, B, and C can be started as soon as possible. b. All of the tasks A, B and C should be finished first before task F can be started. c. All of the tasks A through H should be finished first before task I can be started. d.All of the tasks B, E, C and F should be finished first before task H can be started. Answer the two questions please.1. Which of the following is the key identifier of a resource-allocation problem? I. Constraints with the form " Amount of resource used => Amount of resource available" II. Constraints with the form " Amount of resource used <= Amount of resource available" III. Constraints with the form " Level achieved => Minimum acceptable level" IV. All constraints have the form " Amount provided = Required amount" a. I only b. II only c. III only d. IV only e. At least two is correctA consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…
- The Mechanical Engineering department has a student team that is designing a formula car for national competition. The time required for the team to assemble the first car is 100 hours. Their improvement (or learning rate) is 0.8, which means that as output is doubled, their time to assemble a car is reduced by 20%. Use this information to determine: the time it will take the team to assemble the 10th car. Create an excel spreadsheet having the following table. You must show the formula used in the excel sheets to calculate values in the columns. Plot Number of Units vs Time (in hours) and Number of Units vs Cumulative Time (in hours) in the same plot. Use different colors to distinguish the data.The Mechanical Engineering department has a student team that is designing a formula car for national competition. The time required for the team to assemble the first car is 100 hours. Their improvement (or learning rate) is 0.8, which means that as output is doubled, their time to assemble a car is reduced by 20%. Use this information to determine: the time it will take the team to assemble the 10th car. Create an excel spreadsheet having the following table. You must show the formula used in the excel sheets to calculate values in the columns. Plot Number of Units vs Time (in hours) and Number of Units vs Cumulative Time (in hours) in the same plot. N (no of Units) Time to Produce Nth Cumulative Time (1 to N) 1 2 3 4 5 6 7 8 9 10In a calculated financial maneuver, E-Power Inc. has acquired a new manufacturing facility for producing small electric motors. You have been asked to provide an answer to the following question: How many new personnel should be hired and trained, or laid off, over each of the next six months? The labor requirements and monthly wage rates for trained employees are given in the following table. Trainees can be hired at the beginning of each month. One consideration to take into account is that workers must have one month of classroom instruction before they can work in manufacturing. Therefore, a trainee must be hired a month before the worker is actually needed. Each classroom student uses 60 hours of a trained employee’s time, so there are 60 fewer hours available for manufacturing. Each trained employee can work up to 180 hours a month (total time, instructing plus in manufacturing). Management may lay off at most 15% of the trained employees at the beginning of the month, but…
- A project director runs a staff consisting of 6 scientists and 3 lab technicians. Three new projects have to be worked on and the director decides to assign 4 of her staff to the first project, 3 to the second, and 2 to the third. In how many ways can this be accomplished if each project requires 1 lab technician?Please answer parts d,e,f,g,h,i of the the word problem below. The answers for parts a, b,c are written below so could you continue to answer the questions.Nice-Fit is a (fictional) small business producing outfits for costume parties and specialoccasions. Custom designs can be tailored to a customer’s request. Tom and Ann are theowners of the company and source all the fabric, design the outfits and make the costumesthemselves. Tom and Ann keep spreadsheets with information on the material purchased andcostumes made, but they find it difficult to keep track of their products, raw materials, andsales. The raw materials are supplied from a fabric company in India, and the production takesplace in a manufacturing company in China. The clothing is sold at local weekend markets,sold, or rented through costume hire shops, and sold at their physical store. Tom and Annreceive a small percentage of the sales and rentals of their costumes from the hire shops.They have no information on customers other than those who request custom designsdirectly from them. In 2020, the Covid-19 pandemic had a major impact on global economies,businesses and how we…