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Kars Department Store located in a business area has three types of employees for any given day: sales associate, sales representative, and supervisor. Sales associates handle sales transactions and keep the shelves organized. Sales representatives can handle all of the tasks of sales associates. They also deal with customer problems, product changes and product returns. Supervisors can perform all the tasks of sales representatives except for customer problems. Only sales representatives handle customer problems. Supervisors oversee and train all employees. Sales associates are 65% as productive as supervisors are. Sales representatives are 80% productive as Supervisors. Pay rates for the sales associate, sales representative, and supervisor are $250, $340, and S420, respectively per weekend. There has to be at least three sales representatives to handle all customer problems. There also must be at least 1 supervisor on duty. The company's policy is to have at least one associate and/or representatives for every 3 sales associates on weekends. Weekends are especially busy. They are looking to hire people to work only on weekends. They need the equivalent of 11 supervisors on weekends. a. Formulate the Integer programming model. b. Solve the model to find the optimal number of workers in each category c. How many workers of each type are needed? What is the total cost? d. Recent weekends were busier than expected. What would be the impact on cost of increasing the number of equivalent supervisors to 12? e. Management believes there has been inadequate oversight of sales associates. What would be the impact on cost if the policy were at least one associate and/or representatives for every two sales associates on weekends? (Stay with the equivalent of only 11 supervisors) Kars Department Store located in a business area has three types of employees for any given day: sales associate, sales representative, and supervisor. Sales associates handle sales transactions and keep the shelves organized. Sales representatives can handle all of the tasks of sales associates. They also deal with customer problems, product changes and product returns. Supervisors can perform all the tasks of sales representatives except for customer problems. Only sales representatives handle customer problems. Supervisors oversee and train all employees. Sales associates are 65% as productive as supervisors are. Sales representatives are 80% productive as Supervisors. Pay rates for the sales associate, sales representative, and supervisor are $250, $340, and S420, respectively per weekend. There has to be at least three sales representatives to handle all customer problems. There also must be at least 1 supervisor on duty. The company's policy is to have at least one associate and/or representatives for every 3 sales associates on weekends. Weekends are especially busy. They are looking to hire people to work only on weekends. They need the equivalent of 11 supervisors on weekends. a. Formulate the Integer programming model. b. Solve the model to find the optimal number of workers in each category c. How many workers of each type are needed? What is the total cost? d. Recent weekends were busier than expected. What would be the impact on cost of increasing the number of equivalent supervisors to 12? e. Management believes there has been inadequate oversight of sales associates. What would be the impact on cost if the policy were at least one associate and/or representatives for every two sales associates on weekends? (Stay with the equivalent of only 11 supervisors)