1. A manufacturer of industrial motors has identified ten new prospective customers for its products and estimated each customer's annual sales potential as follows:
Customer 1 2 3 4 5 6 7 8 9 10
Sales Potential
(in $1,000,000s) $113 $106 $84 $52 $155 $103 $87 $91 $128 $131
The company would like to allocate these ten prospective customers to five of its current salespeople in the most equitable way possible. (Each customer may be assigned to only one sales person.) To do this, ideally, the customers assigned to each of the five salespeople would have exactly the same sales potential. If such a solution is not possible, the company would like to minimize the total amount by which the actual sales potentials for the customers assigned to each salesperson deviate from the ideal allocation.
a. Ideally, what sales potential should be assigned to each salesperson?
b. Formulate a mathematical programming model for this problem.
c. Implement your model in a spreadsheet and solve it.
d. What is the optimal solution and the optimal objective value?
e. Suppose we instead want to minimize the maximum amount by which any salesperson's assigned sales potential deviates from the ideal allocation. What is the optimal solution and optimal objective value?