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Linear Programming Problem 1. Linear Programming Problem - Use Excel Solver A company that makes capacitors has three 8-hour manufacturing shifts during the day: Shift 1: 8 am - 4 pm Shift 2: 4 pm - midnight Shift 3: midnight - 8 am The company wants to maximize profit, and hires you to determine how many workers to employ in each shift. The company gives you the following information: -It is estimated that 1 worker would make 10 capacitors per shift; The workers' hourly salaries are $12, $16, and $20 for Shift 1, 2, and 3, respectively; -It is determined that the average numb er of defects p er capacitor varies with shift as follows: 4 defects/capacitor during Shift 1, 3 defects/capacitor during Shift 2, and 2 defects/capacitor during Shift 3 -Due to these defects, the capacitors made in the different shifts will be sold at different prices: $18/capacitor made in Shift 1, $22/capacitor made in Shift 2, and $24/capacitor made in Shift 3 The company has the following constraints: 1. They have a total of 25 workers (and they do not want to hire more); 2. They want to schedule no more than 10 workers per shift; 3. The average number of defects per capacitor for a day of production cannot exceed 3; 4. At most 250 capacitors can be sold each day. a) Setup the linear programming problem List the decision variables 1. Hint: there are 3 decision variables; - 2. Define the objective function Hint: the profit per shift will be based on the sales price of capacitors made on a - particular shift minus the total - 8-hr - cost for the workers in that shift; 3. Define the constraints - Hint 1: there are 4 constraints, -Hint 2: defects per capacitor per day can be calculated by total defects on all shifts/total capacitors produced that day and must be at most 3 b) Using Excel Solver, determine the optimal number ofworkers in each shift to maximize profit Turn in your Excel file. Linear Programming Problem 1. Linear Programming Problem - Use Excel Solver A company that makes capacitors has three 8-hour manufacturing shifts during the day: Shift 1: 8 am - 4 pm Shift 2: 4 pm - midnight Shift 3: midnight - 8 am The company wants to maximize profit, and hires you to determine how many workers to employ in each shift. The company gives you the following information: -It is estimated that 1 worker would make 10 capacitors per shift; The workers' hourly salaries are $12, $16, and $20 for Shift 1, 2, and 3, respectively; -It is determined that the average numb er of defects p er capacitor varies with shift as follows: 4 defects/capacitor during Shift 1, 3 defects/capacitor during Shift 2, and 2 defects/capacitor during Shift 3 -Due to these defects, the capacitors made in the different shifts will be sold at different prices: $18/capacitor made in Shift 1, $22/capacitor made in Shift 2, and $24/capacitor made in Shift 3 The company has the following constraints: 1. They have a total of 25 workers (and they do not want to hire more); 2. They want to schedule no more than 10 workers per shift; 3. The average number of defects per capacitor for a day of production cannot exceed 3; 4. At most 250 capacitors can be sold each day. a) Setup the linear programming problem List the decision variables 1. Hint: there are 3 decision variables; - 2. Define the objective function Hint: the profit per shift will be based on the sales price of capacitors made on a - particular shift minus the total - 8-hr - cost for the workers in that shift; 3. Define the constraints - Hint 1: there are 4 constraints, -Hint 2: defects per capacitor per day can be calculated by total defects on all shifts/total capacitors produced that day and must be at most 3 b) Using Excel Solver, determine the optimal number ofworkers in each shift to maximize profit Turn in your Excel file