Reference no: EM132070731

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 Table. Type of Operation 1 2 3 4 Profit ($) 200 150 100 80 X-ray time (minutes) 6 5 4 3 Laboratory time (minutes) 5 4 3 2 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 while 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: 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. The cost per unit deviation from each goal is as follows: Goal 1 Cost of $1 for each dollar by which profit goal is unmet Goal 2 Cost of $10 for each hour by which X-ray goal is unmet Goal 3 Cost of $8 for each hour by which laboratory goal is unmet Formulate a goal programming model to minimize the daily cost incurred due to failing to meet the hospital