A company wants to assign ten salesmen to eight different sales zones. The expected profit from each salesman differs from one zone to another based on their experience with the different customers in the respective zone. The company needs at least one salesman to be assigned to each zone. The following table shows the expected revenue per month in $1,000 of each salesman in the different zones.

Zone (revenue, in thousands of dollars)
Salesman A B C D E F G H 1 3 12 3 5 9 3 12 4 2 3 4 5 9 11 10 10 10 3 3 8 11 6 10 3 8 3 4 7 11 7 3 8 11 5 4 5 5 4 12 8 3 11 11 5 6 7 10 3 4 4 12 9 6 7 11 6 7 5 6 7 3 4 8 11 6 5 4 9 5 10 12 9 9 8 10 4 3 4 3 12 10 4 6 8 8 5 12 6 12 The company wants optimal assignment that maximizes the expected revenue.

a. Formulate a linear programming model to this problem.

b. Solve the problem using computer.