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Problem 2 . A hospital outpatient clinic performs four types of operations. The profit per operation, as well as the minutes of X-ray time and laboratory time used, are given in the table below. The clinic has 500 private rooms and 500 intensive care rooms. Type 1 and type 2 operations require a patient to stay in an intensive care room for one day, whereas type 3 and type 4 operations require a patient to stay in a private room for one day. Each day, the hospital is required to perform at least 100 operations of each type. The hospital has set the following goals (listed in order of priority): ? Goal 1: Earn a daily profit of at least$100,000. ? Goal 2: Use at most 50 hours daily of X-ray time. ? Goal 3: Use at most 40 hours daily of laboratory time. Use goal programming to determine the types of operations that should be performed.

WNF Profit $200 $150 $100 $80 4 X-ray time (minutes) 6 5 4 3 Lab time (minutes) 5 4 3 2 6 Op 1 Op 2 Op 3 Op 4 8 Performed >= >= >= 10 Needed 11 12 Rooms used Available 13 Private = 19 X-ray (minutes) =