Based on Charnes and Cooper (1955). A small company is trying to determine employee salary based on the following attributes: effectiveness, responsibility, initiative, experience, education, self-expression, planning ability, intelligence, and the ability to get things done. Each of the company’s seven executives has been rated on each of these attributes, with the ratings shown in the file P04_86.xlsx.

The company wants to set each executive’s salary by multiplying a weight for each attribute by the executive’s score on each attribute. The salaries must satisfy the following constraints:

■ The salary of a lower-numbered executive must be at least as large as the salary of a higher-numbered executive.

■ Executive 1’s salary can be at most $160,000 and executive 7’s salary must be at least $40,000.

■ The salaries of executives 1, 5, and 7 should match $160,000, $100,000, and $40,000, respectively, as closely as possible.

■ All attribute weights must be nonnegative.

Develop a method for setting salaries. [For executives 1, 5, and 7, define “over” and “under” decision variable cells and add a constraint such as Executive 5 salary + (Amount executive 5 salary under $100,000) – (Amount executive 5 salary over $100,000) = $100,000. Then the objective cell to minimize is the sum of over and under decision variable cells for positions 1, 5, and 7. If you did not include the over and under decision variable cells, why would your model fail to be linear?]