Based on Welling (1977). The Touche Young accounting firm must complete three jobs during the next month. Job 1 will require 500 hours of work, job 2 will require 300 hours, and job 3 will require 100 hours. At present, the firm consists of five partners, five senior employees, and five junior employees, each of whom can work up to 40 hours per week. The dollar amount (per hour) that the company can bill depends on the type of accountant assigned to each job, as shown in the file P16_07.xlsx. (The “X” indicates that a junior employee does not have enough experience to work on job 1.) All jobs must be completed.

Touche Young has also set the following goals, listed in order of priority:

■ Goal 1: Monthly billings should exceed $74,000.

■ Goal 2: At most one partner should be hired.

■ Goal 3: At most three senior employees should be hired.

■ Goal 4: At most one junior employee should be hired.

Use goal programming to help Touche solve its problem.