this is a goal programming problem . please formulate it only

QUESTION 1 Due to COVID-19 pandemic, a hospital wants to set its plan to well manage the current situation. The hospital divides COVID-19 patients into three types. The cost per patient type, as well as the minutes of PCR test time, and the nurses needed, are given in the following table: Type of COVID-19 Patient 1 2 3 Cost (S) 500 400 250 PCR test (hours) 0.2 0.15 0.1 Nurses needed (person) 2 1 1 The hospital has 500 private rooms and 300 intensive care rooms. Patients Type 1 and Type 2 are required to stay in an intensive care room while Type 3 patients are required to stay in a private room. The hospital is planning to accept at least a total of 150 patients of Type I and Type 2 combined, and at least a total of 50 patients of Type 3. The hospital has set the following goals: Goal I Use a budget of at most $100,000. Goal 2 Use at least 50 hou of PCR test time. Goal 3 Allocate exactly 400 nurses to serve the accepted patients. The cost per unit deviation from each goal is as follows: Goal 1 Cost of S1 for each dollar by which budget goal is unmet. Goal 2 Cost of $12 for each hour by which PCR test goal is unmet. Goal 3 Cost of $100 for each person by which nurse allocation goal is overachieved, while the cost for each person by which nurse allocation goal is underachieved is $70. Formulate a goal programming model to minimize the total cost incurred due to failing to meet the hospital's goals