For this question, please formulate the problem as a linear model with clearly stated decision variables, objective functions, and constraints. Please attach the formulations. Please also find the optimal solutions, while also showing slack or surplus variables at each optimal solution.

Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $64 per day, and a temporary operator is paid $42 per day. The company wants to determine the number of permanent and temporary operators to hire to minimize costs. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis