A hospital administrator is reviewing departmental requests prior to the design of a new emergency room....

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A hospital administrator is reviewing departmental requests prior to the design of a new emergency room. At issue is the number of beds for each department. The current plans call for a 15,000-square-foot facility and a budget of $300,000. The following table summarizes other relevant data: Type of Bed Major Trauma Surgical Medical Number of Beds Requested 20 20 Cost per Bed (including equipment) $12,600 $5,400 $8,600 Area per Bed (square feet) 474 542 438 Peak Requirements (maximum number of patients at one time) 3 18 15 The hospital board has established the following four goals (in decreasing order of priority): 1) Devise a plan that requires at most 15,000 square feet. 2) Meet or exceed peak requirements. Note: Surgical and Medical can be interchanged (mixed), but Major Trauma patients cannot use other facilities. 3) Spend no more than the $300,000 budget. 4) Meet or exceed the departmental requests. a) Formulate a goal programming model the hospital administrator can use to decide how many beds each department should have in the new emergency room. Define your decision variables clearly together with the deviation variables for each goal, state the goal programming objective function, and all the relevant (goal and/or structural) constraints. Do not solve the model. (9 marks) b) What modifications to your goal program are necessary if the third goal were restated as "Minimize the cost of the new emergency room"? Note: For part (e) and (d), you do not need to rewrite the entire model, only mention the modifications that are relevant. Also, you do not need to solve the revised model. (1.5 marks) c) What modifications to your goal program are necessary if a fifth goal is added stating that "If the first goal is not achieved, the amount above 15,000 square feet should be at most 1000"? (1.5 marks) A hospital administrator is reviewing departmental requests prior to the design of a new emergency room. At issue is the number of beds for each department. The current plans call for a 15,000-square-foot facility and a budget of $300,000. The following table summarizes other relevant data: Type of Bed Major Trauma Surgical Medical Number of Beds Requested 20 20 Cost per Bed (including equipment) $12,600 $5,400 $8,600 Area per Bed (square feet) 474 542 438 Peak Requirements (maximum number of patients at one time) 3 18 15 The hospital board has established the following four goals (in decreasing order of priority): 1) Devise a plan that requires at most 15,000 square feet. 2) Meet or exceed peak requirements. Note: Surgical and Medical can be interchanged (mixed), but Major Trauma patients cannot use other facilities. 3) Spend no more than the $300,000 budget. 4) Meet or exceed the departmental requests. a) Formulate a goal programming model the hospital administrator can use to decide how many beds each department should have in the new emergency room. Define your decision variables clearly together with the deviation variables for each goal, state the goal programming objective function, and all the relevant (goal and/or structural) constraints. Do not solve the model. (9 marks) b) What modifications to your goal program are necessary if the third goal were restated as "Minimize the cost of the new emergency room"? Note: For part (e) and (d), you do not need to rewrite the entire model, only mention the modifications that are relevant. Also, you do not need to solve the revised model. (1.5 marks) c) What modifications to your goal program are necessary if a fifth goal is added stating that "If the first goal is not achieved, the amount above 15,000 square feet should be at most 1000"? (1.5 marks)