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Foster School of Business, University of Washington BUS AN 507 2022 Summer BUS AN 507: Spreadsheet Modeling for Business Enterprise 2022 Summer Problem Set #1 Individual Submission Due by Saturday, July 16, 11:59 p.m. Team Submission Due by Monday, July 18, 11:59 p.m. Instructions: 1. Solve each problem in separate tabs in a single Excel file. Label the tabs by problem number. For each problem, formulate a linear programming spreadsheet model and solve it using Solver. 2. Submit your individual solution to Canvas. Then, meet with your study group and discuss your various solutions. Create a single submission. Only one member of your group should submit it to Canvas no later than the team submission due date and time shown above. 1. A Production Problem (LP) Management of Delta Manufacturing Company is considering allocating excess production capacity to one or more of three products, Products 1, 2, and 3. Each product should be processed sequentially through machines A, B, and C. For example, to produce one unit of Product 1, it requires 9 hours first with machine A, then 5 hours with machine B, and finally 3 hours with machine C. The number of machine-hours required for each unit of the respective products are shown in the next table. Product 1 Product 2 Product 3 Available Machine Hours Machine A 9 3 5 500 Machine B 5 4 0 350 Machine C 3 0 2 150 The sales department indicates that as many Products 1 and 2 as possible can be sold to the end consumers, while the market size for product 3 is at most 20 units per week. Furthermore, the management does not want the output of Product 1 to be more than 60% of the total output of all three products. The unit profit would be $50, $20, and $25, respectively. The objective is to determine how much of each product that the company should produce to maximize the total profit. 2. A Transportation Problem (LP) The Happy Little Sheep (HLS) Company has three plants producing child car seats that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive at least 10 shipments per month. The distance (miles) from each plant to the respective distribution center is given below. 1 Foster School of Business, University of Washington BUS AN 507 2022 Summer DC 1 DC 2 DC 3 DC 4 Plant 1 800 1300 400 700 Plant 2 1100 1400 600 1000 Plant 3 600 1200 800 900 The freight cost for each shipment is $100 per shipment plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? Formulate this problem on a spreadsheet and then use Solver to obtain an optimal solution. 3. The Human Resources Scheduling Problem (Linear Programming) In 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. Jan Feb Mar Apr May Jun Monthly Wage Rate $3,800 $3,800 $4,000 $4,000 $4,200 $4,200 Mfg. Hours Required 8,000 7,600 9,100 10,200 9,300 7,600 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 must pay one-half-month’s wage for severance pay. A trainee is paid 40% of regular wages for a trained employee during their training month. There are 46 trained employees available at the beginning of January. Formulate this hiring-andtraining-and-layoffs model as a linear programming spreadsheet model. 2