Problem 5-01 The hospital administrators at General Hospital, University Hospital, County Hospital, and State Hospital have been meeting to discuss ways in which they can help one another to improve the performance at each of their hospitals. A consultant suggested that they consider using DEA to measure the performance of each hospital relative to the performance of all four hospitals. In discussing how this evaluation could be done, the following three input measures and four output measures were identified: ANNUAL RESOURSES CONSUMED (INPUTS) BY THE FOUR HOSPITALS Input measure Hospital General University Country State Full-time equivalent nonphysicians Supply expence ($1000s) Bed-days available ($1000s) 285.20 123.80 106.72 162.30 128.70 64.21 275.70 210.40 348.50 154.10 104.10 104.04 ANNUAL SERVICES PROVIDED (OUTPUTS) BY THE FOUR HOSPITALS Hospital Output measure General University Country State Medicare patient days (1000s) 48.14 34.62 Non-Medicare patient days (1000s) 43.10 27.11 Nurses trained Interns trained 253 41 148 27 36.72 33.16 45.98 56.46 175 23 160 84 a. Use these data to develop a linear programming model that could be used to evaluate the performance of General Hospital. Round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. If your answer is zero, enter "0". If the constant is "1" it must be entered in the box. Let E = the fraction of General Hospital's input available to the composite hospital wg = weight applied to inputs and outputs for General Hospital wu = weight applied to inputs and outputs for University Hospital wc weight applied to inputs and outputs for County Hospital ws = weight applied to inputs and outputs for State Hospital Min E s.t wg + wu + wc + WS wg + 34.62 wu + WC + 33.16 ws 43.10 wg + wu + WC + ws wg + 148 wu + WC + 160 ws 41 wg + wu + WC + WS E+ -123.80 E+ E+ 285.20 wg + wg + 106.72 wg + wu + 275.70 wc + WS 128.70 wu + WC + 154.10 ws wu + 104.10 wc + Ws wg, wu, wc, WS 0 b. The following solution is optimal. Objective Function Value = 1.000 Variable Value Reduced Cost E 1.000 0.000 WG 1.000 0.000 WU 0.000 0.000 WC 0.000 0.331 WS 0.000 0.215 Does the solution indicate that General Hospital is relatively inefficient? No c. Which hospital or hospitals make up the composite unit used to evaluate General Hospital? General Hospital Explain why? The input in the box below will not be graded, but may be reviewed and considered by your instructor.