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 (in minutes) required by the various operators to perform the required operations on each machine are summarized in the table below. Joe wants to assign one operator to each machine so that the total operating time for all three operators is minimized.

Times Drill Lathe Grinder

Operator1 18 22 35

Operator2 30 41 28

Operator3 36 25 18

a. Formulate a linear programming model for this problem b. Solve the model using SOLVER c. Joe’s brother, Fred, has asked him to hire his wife, Kathy, who is a machine operator. Kathy can perform each of the required machine operations in 25 minutes. Should Joe hire his sister-in-law? Hint - define a variable for each machine-operator pair which is = 1 if that operator is on that machine = 0 if that operator is not on that machine (This is a special case of the TRANSPORTATION PROBLEM (Class 4) with SUPPLY and DEMAND are all equal to 1. Do not have to put into SOLVER that the variables have to be integer; it always happens.) (Hint: D1 + L1 + G1 ≤ 1 D1 + D2 + D3 ≥ 1 6 constraints in total)