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Linear Programming - Simplex Method

Kay Manning is a sales manager with two salespeople working for her. The ability of each salesperson to secure new accounts has historically been: Jesse Burkett can generate 4 new accounts per 10 visits to prospects, and Ed Delahanty averages 3 new accounts per 10 visits to prospects. As of May 1, Jesse has 20 established customers that he must call on each month if he is to retain their monthly orders. Ed has 15 established accounts to maintain.

The average time each salesperson spends with each type of customer per visit is:

Type of Customer

Salesperson New Account Established Account
Jesse 10 5
Ed 8 6

Each new order yields the company an average profit of $150, while orders from established accounts are usually smaller and yield an average profit of $50 an order. Jesse has a larger area to cover than Ed, and therefore Jesse only has 120 hours (outside of travel time) to spend with customers each month. Ed has 135 hours available to spend with customers.

a) Formulate a linear programming model to determine how many new and how many old customers each salesperson should call on in May to maximize profits.
b) Solve the problem by the simplex method.

Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.