6 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 of work, and job 3 will require 100 hours of work. Currently, the firm consists of 5 partners, 5 senior employees, and 5 junior employees, each of whom can work up to 40 hours per month. The dollar amount (per hour) that the company can bill depends on the type of accountant who is assigned to each job, as shown in Table 60. (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 $68,000.

Goal 2 At most, 1 partner should be hired.

Goal 3 At most, 3 senior employees should be hired.

Goal 4 At most, 5 junior employees should be hired.

Formulate a preemptive goal programming model for this situation.

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TABLE 59 Head Chuck Mutton Moisture Fat (per lb) .05 Protein (per lb) .20 Cost (in c) .12 220 .24 .11 0 .26 .08 0 9 8 0