Deanna MacCormac Paige Nielsen ________________________________________________________________________________ _ BUSI 410 – Homework #1 Due Feb. 2nd Instructions: Solve each of the following problems using these steps (1) Identify the objective of the firm/manager as specified in the problem. (2) Identify the decision variables in the problem. (3) Identify the constraints in terms of the decision variables. (4) State the objective and the constraints in English and then convert them into mathematical functions in terms of the decision variables. (5) Set up the problem in Excel and use Solver to find the optimal values of the decision variables. Ask Solver to create an Answer Report and, if necessary, a Sensitivity Report. (6) Answer the questions in each of the problems below. (7) Please submit the following: a) your mathematical formulation, where you clearly specify the notation you are using, b) Solver’s Answer Report, c) Solver’s Sensitivity Report only if you used it , and d) your written answers to step 6 above. Please do not submit your spreadsheet setup. 1. The staff demand at UNC student store in terms of hours per week is given below: Week Staff Demand (hours) 1 225 2 265 3 270 4 185 At the beginning of each week, the store hires students to fulfill its staff demand. Students hired in week 1 work for 3 consecutive weeks (i.e., a student hired in week 1 works for weeks 1, 2 and 3); each of these students works for 15 hours per week and is paid $450 in total. Students hired in weeks 2 and 4 work only for 1 week; each of them works for 20 hours per week and is paid $180 in total. Students hired in week 3 work for 2 weeks; each of them works for 15 hours per week and is paid $290 in total. In each week, the student store needs to have total student working hours no less than its weekly demand described in the table above. a. Formulate a linear programming model to determine UNC student store’s optimal hiring plan (i.e., the number of students hired at the beginning of each week) to minimize its total cost. (8pts) b. Solve the model using Excel Solver. (4pts) 1
_________________________________________________________________________________________________ BUSI 410 – MacPherson Refrigeration Limited To produce units in regular time, there have to be enough capacity (sufficiently many workers). Note that we know workers' productivity (480/12 = 40 units per month) in regular time. We assume that productivity remains the same in overtime. Since overtime cost is defined based on worker-month ($3300 per worker-month), for every unit produced in overtime, the incurred overtime cost is $3300/40 = $82.5. The case discusses three possible alternatives the company could follow to meet forecasted demand. In preparation for the case discussion, please do the following: A. Prepare answers to the following questions: 1. What are the pros and cons of alternative 1 (Exhibit 1)? 2. What are the pros and cons of alternative 2 (Exhibit 2)? 3. What are the pros and cons of alternative 3 (Exhibit 3)?