The manager of the Ewing and Barnes Department Store has four employees available to assign to three departments in the store€”lamps, sporting goods, and linens. The manager wants each of these departments to have at least one employee, but not more than two. Therefore, two departments will be assigned one employee, and one department will be assigned two. Each employee has different areas of expertise, which are reflected in the daily sales each employee is expected to generate in each department, as follows:

The manager wishes to know which employee(s) to assign to each department in order to maximize expected sales.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
c. Suppose that the department manager plans to assign only one employee to each department and to lay off the least productive employee. Formulate a new linear programming model that reflects this new condition and solve by using thecomputer.

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Department Sales Employee Laps Sporting Goods Linens $ 90 100 140 160 $130 275 180 200 $150 300 225 120