Question: A manufacturer of industrial motors has identified
A manufacturer of industrial motors has identified ten new prospective customers for its products with estimated each customer’s annual sales potential as follows:
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. (Hint: For each salesperson, create two decision variables to represent the amount by which his or her assigned sales potential is, respectively, under or over the ideal sales potential.)
c. Implement your model in a spreadsheet and solve it.
d. What is the optimal solution?
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