BUSI 410 Homework 1 Instructions 1 For question Formulate a linear programming model a Clearly define the decision variables in the problem b Define the objective of the firm manager as a function of the decision variables c Specify the constraints using the decision variables d You can ignore any integrality requirements in this homework see Putting Linear Programming into Practice on page 11 of the CP for a discussion on why relaxing integer constrains in various situations may be reasonable e Explicitly type up your entire LP formulation in Word 2 For question Solve the model using Excel Solver a Set up the problem in Excel and use Solver to solve the linear program b Create and paste your Answer Report do not submit the spreadsheet formulation 3 Submit answers to other questions if any and paste a Sensitivity Report only if you used it in answering these questions 4 If you need help typing mathematical formulae read Creating Word and PDF Documents in Canvas Files Miscellaneous Submit the entire assignment as a single Word PDF file not an Excel spreadsheet Include all group members names in the file 1 The staff demand at UNC Student Stores for the 4 busiest consecutive weeks of a year is given below Week 1 2 3 4 Staff Demand hours 330 450 390 410 The store hires students to fulfill its staff demand in these weeks Students hired at the beginning of weeks 1 or 3 work for 2 consecutive weeks e g a student hired in week 1 works for weeks 1 and 2 in each week each student works for 15 hours and is paid 200 Students hired at the beginning of week 2 work for 3 consecutive weeks in each week each student works for 10 hours and is paid 100 Students hired at the beginning of week 4 work only for 1 week each student works for 5 hours 1 and is paid 65 In each week Student Stores 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 Student Store s optimal hiring plan i e the number of students hired at the beginning of each week to minimize its total cost 21pts b Solve the model using Excel Solver 2pts c Students hired in weeks 1 and 3 work for 15 hours per week in 2 consecutive weeks and are paid 200 per week Does this lead your optimal solution to hire the same number of students in weeks 1 and 3 If not in which week do you hire more students Do you have an intuitive explanation why this is the case 5pts d In this year week 4 coincides with a national holiday as a result there is more staff demand in week 4 Suppose week 4 s staff demand for this year is 430 hours instead of the normal 410 hours Without re solving your optimization model please answer the following questions you need full justification to receive full credit i ii Does the total cost change If so by how much 5pts Do you now hire a different number of students in the optimal solution How do you know 5pts 2 You just won a 100 000 lottery and are considering the following investment vehicles Investment Global currency mutual fund GF Energy mutual fund EF Certificate of deposit CD Annual Return Rate 8 5 3 You want to maximize your return from investment in terms of dollars one year from now while meeting the following guidelines Your total investment cannot exceed 100 000 You cannot short any investment i e you cannot invest in a negative amount You must invest at least 5 000 in GF and at least 3 000 in EF The amount invested in EF should not exceed the amount invested in No more than 80 of the investment can be in GF and CD combined EF and CD combined should account for at least 30 of your CD investment 2 a Formulate a linear programming model for your investment decision b Solve the model using Excel Solver 2pts c Suppose EF s return is increased to 9 which is higher than GF s Without resolving the problem can you tell if it is optimal to invest more in EF than in GF 4pts ii What do you think is causing this 4pts You need full justification to receive full credit 26pts 8 i ii 3 3 Orange Company is allocating its advertising budget for its new smartphone targeting graduate and undergraduate students in RTP The company has invited representatives from the local radio station television station and newspaper to make presentations in which they describe their audiences The television station representative indicates that a TV commercial which costs 15 000 would reach 25 000 potential customers per ad The breakdown of the audience is as follows Fema le 5 000 10 00 0 Fema le 3 000 1 000 Fema le 1 500 7 500 Male Graduate Undergraduate 5 000 5 000 Graduate Undergraduate 4 000 2 000 Graduate Undergraduate 1 500 4 500 Male Male 4 The newspaper representative claims to be able to provide an audience of 10 000 potential customers at a cost of 4 000 per ad The breakdown of the audience is as follows The radio station representative says that every radio commercial has an audience of 15 000 at a cost of 7 000 The breakdown of the audience is as follows Orange Company has the following advertising policy The number of radio commercials must be at least twice the number of newspaper ads The advertising campaign must reach at least 80 000 customers The size of the undergraduate audience must be at least twice the size of the graduate audience At least 40 of the audience must be female Available space limits the number of newspaper ads to at most two Orange Company wants to know the optimal number of each type of advertising to purchase to minimize total cost a Formulate a linear programming model to determine the company s advertising strategy 24pts b Solve the model using Excel Solver 2pts 5