1. Your consulting team has been hired to help support decision making for the next Coldplay's tour. A first decision problem relates to selecting which guitars to bring to the tour, given that the tour bus has a weight limit and different sponsors for the guitar brands are willing to pay for having their guitars played by the band ("income" column on Table 1). The following table presents all the relevant information needed to formulate the problem. Guitar ID Brand Model Weight (LB) Income 1 Paul Reed Smith Custom 24 7 2200 2 Paul Reed Smith SE 6 2500 3 Fender Telecaster 8 2700 4 Fender Stratocaster 7 2600 5 Gibson Les Paul 11 3000 6 Gibson Memphis 10 2900 The tour manager has established the following guidelines: The maximum weight available for guitars is 35 LBs If guitar 1 is selected, then guitars 3 or 5 must be also selected If guitar 2 is selected, then guitars 3 and 5 must be also selected At least 1 guitar from each brand should be selected The goal of the tour manager is to maximize profit. 1. (70) Formulate the problem as a integer (linear) program by following these steps: a. (5) Precisely define decision variables for the model b. (5) State the objective function c. (5) State the constraint(s) that ensure that the maximum weight available for guitars is 35 LBs d. (5) State the constraint(s) that ensure that if guitar 1 is selected, then guitars 3 or 5 must be also selected e. (5) State the constraint(s) that ensure that if guitar 2 is selected, then guitars 3 and 5 must be also selected f. (10) State the constraint(s) that ensure that at least 1 guitar from each brand should be selected A second decision problem relates to assigning guitars to songs (considering all the previous variables, constraints, objective already established). The following table presents the ordered set list and which guitars can be used to play any given song. Position Song name Suitable guitars 1 Yellow 1,3,5 2 Fix you 1,2,6 3 Everglow 1,3,4 4 The scientist 2,3,4 5 In my place 3,5,4,6 6 Adventure of a lifetime 1,4,6 Every song should have assigned a suitable guitar (and of course, that guitar should be selected to be in the tour!) and no guitar should be used to play more than 2 consecutive songs. g. (5) Define new variables needed (assume that the model already includes all the variables and constraints defined before.) h. (15) State the constraint(s) that ensure that every song should have assigned a suitable guitar and you can only assign a guitar to a song if the guitar has been selected to be used in the tour i. (15) State the constraint(s) that ensure that no guitar should be used to play more than 2 consecutive songs