# Excel Linear Programming

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 claims 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
B. Solve this problem using graphical analysis

### Comments for Excel Linear Programming

 May 28, 2011 Excel Linear Programming - Graphical Analysis by: Staff ---------------------------------------------- Part IV Condition 1: 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. 16*P + 12*T ≥ 450 16*20 + 12*10 ≥ 450 320 + 120 ≥ 450 440 is not ≥ 450, this doesn’t quite meet the criteria Condition 2: The Company has 40 computer workstations. P + T ≤ 40 20 + 10 ≤ 40 30 ≤ 40, OK Condition 3: The Company wants to limit claims with errors to 25 per day. 0.5*P + 1.4*T ≤ 25 0.5*20 + 1.4*10 ≤ 25 10 + 14 ≤ 25 24 ≤ 25, OK Conditions 4 & 5: The values of P & T are both positive. ----------------------------------------------- The final answers to your question: A. Formulate a linear programming model for this P = number of permanent operators T = number of temporary operators C = cost Minimize the objective function C = 64*P + 42*T Subject to 16*P + 12*T ≥ 450 P + T ≤ 40 0.5*P + 1.4*T ≤ 25 P ≥ 0 T ≥ 0 -------------------------- B. Solve this problem using graphical analysis The lowest cost (\$1700 per day) occurs when P = 20 and T = 10 However, these are rounded values. One of the boundary conditions is violated using these numbers. The volume is only ≥ 440 per day. The volume should be ≥ 450 per day If you hire one more temporary employee to correct this problem, the error rate also increases to slightly over 25 errors per day. It’s a business decision. The correct answer depends on what is more important: an error rate of under 25, or a volume of over 450. Thanks for writing. Staff www.solving-math-problems.com