Formulate a linear programming model for this problem.

Joe Henderson runs a small metal parts shop. The shop contains 3 machines–a drill press, a lathe, and a grinder. Joe has 3 operators, each certified to work on all 3 machines. However, each operator performs better on some machines than on others. The shop has a contracted to do a big job that requires all 3 machines. The times required by the various operators to perform the required operations on each machine are summarized as follows: Operator Drill Press (min.) Lathe(min.) Grinder(min.)

1 22 18 35

2 41 30 28

3 25 36 18

Joe Henderson wants to assign one operator to each machine so that the total operating time for all 3 operators is minimized.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

c. Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator. Kelly can perform each of the 3 required machine operations in 20 minutes. Should Joe hire his sister-in-law?