Universal Claims Processors processes insurance claims for large national insurance companies. Most

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Question Answered Universal Claims Processors processes insurance claims for large...

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 elTors 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 in order to minimize costs. a. Formulate a linear programming model for this problem. b.

Solve this model by using graphical analysis.

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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 in order to minimize costs. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

Let X be the number of permanent and Y be the number of temporary operator needed to minimize the cost given the conditions.

So the obtained LPP is given below.

Minimize, Z = $64X+ $42Y

Subject to, 16X+12Y ≥ 450 (Number of claims each day Constraint) X+Y ≤ 40 (Number of workstation Constraint) 0.5X+1.4Y ≤ 25 (Defective claim constraint) X, Y ≥ 0.

Now if we plot this LPP we have this following graph,

Here Red , Blue and Green lines are respectively for three constraints and black one is for objective function.

As we can see that pink area is the feasible region and the objective line touching it for the 1st time at point A but point A is not the solution that is because here X and Y need to be in integers but here for point A they are not. If we Zoom the graph we will have this following graph.

Which shows the point E with coordinates (21,10) is the optimal point and thus the optimal solution is X=21 and Y=10.

Hence the should hire 21 permanent employee and 10 temporary employee to minimize the cost and the minimum cost is ($64*21+$42*10) = $1764.