Joe Henderson runs a small metal parts shop. The shop contains three machines—a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three machines.

However, each operator performs better on some machines than on others. The shop has contracted to do a big job that requires all three 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 three 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 three required machine operations in 20 minutes. Should Joe hire his sister-in-law? LO.1