Question

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, andon 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 errorseach 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 operatoris 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 tominimize costs.

A. Formulate a linear programming model for this
B. Solve this problem using graphical analysis

Answer 1

a.
minimize 64x + 42y
st:
16x + 12y >= 450
x + y <= 40
0.5x + 1.4y <= 25

minimize 64x + 42y
st:
-16x - 12y <= -450
x + y <= 40
0.5x + 1.4y <= 25

Graph and find the area that they inclose.
Find the corner points of that area.
Plug the coordinates of each corner point into the minimizing function to see which will give you the lowest overall cost.