(a) Formulate a linear programming model that can be used to perform data envelopment analysis for hospital E. (Let wa = the weight of hospital A, wb = weight of hospital B, wc = weight of hospital C, wd = weight of hospital D, we = weight of hospital E, wf = weight of hospital F, wg = weight of hospital G, and let EI = the efficiency index.) Min EI s.t. sum of weights wa-wb + wc + wd-we - wf - wg = 1 Full-time equivalent nonphysicians 310wa +278.5wb = 165.8wc + 250wd - 206.4we + 384wf + 530.1wg 32.48 Patient-days (under 65) (1,000) 49.52wa = 55.63wb + 25.77WC + 41.99wd + 55.3we - 81.92wf + 119.7wg 55.3 Nurses trained 291wa + 156wb + 141wc + 160wd + 157we - 285wf + 111wg > 157 Interns trained 47wa + 3w6+26wc + 21wd + 82we + 92wf + 89wg > 82 ET, wa, wb, wc, wd, we, wl, wg 20 (b) solve the model. (EI, wa, wb, wc, wd, we, wr, wg) - (c) Is hospital E relatively inefficient? Yes No What is the interpretation of the value of the objective function? The value of El indicates that Hospital E requires more resources in order to continue producing at its output level. The value of El indicates that all the resources used by Hospital E are required to produce the outputs of Hospital E. The value of ET indicates that Hospital E should have a surplus of resources, based on its output. (d) Which hospitals are involved in making up the composite hospital? (Select all that apply.) Hospital A O Hospital B Hospital Hospital D Hospital E Hospital F Hospital Can you make a general statement about which hospitals will make up the composite unit associated with a unit that is not inefficient? If a hospital Select relatively inefficient, then-Select- A linear programming computer package is needed. The following data from a particular study involving seven teaching hospitals include three input measures and four output measures. Input Measures Full-Time Supply Bed-Days Hospital Equivalent Expense Available Nonphysicians (1000s) (1000s) 310.0 134.60 116.00 B 278.5 114.30 106.80 165.6 131.30 65.52 D 250.0 16.0 94.40 E 206.4 151.20 102.10 F 384.0 217.00 153.70 G 530.1 770.80 215.00 Output Measures Patient-Days Hospital (65 or older) (1000s) Patient-Days (under 65) (1000s) Nurses Trained Interns Trained $5.31 49.52 291 47 B 37.64 55.63 156 3 32.91 25.77 141 26 D 33.53 41.99 160 21 E 32.48 55.30 157 82 LL 48.78 81.92 285 92 G 58.41 119.70 111 89 (a) Formulate a linear programming model that can be used to perform data envelopment analysis for hospital E. (Let wa = the weight of hospital A, wb = weight of hospital B, wc = weight of hospital C, wd = weight of hospital D, we = weight of hospital E, wf = weight of hospital F, wg = weight of hospital G, and let EI = the efficiency index.) Min EI s.t. sum of weights wa-wb + wc + wd-we - wf - wg = 1 Full-time equivalent nonphysicians 310wa +278.5wb = 165.8wc + 250wd - 206.4we + 384wf + 530.1wg 32.48 Patient-days (under 65) (1,000) 49.52wa = 55.63wb + 25.77WC + 41.99wd + 55.3we - 81.92wf + 119.7wg 55.3 Nurses trained 291wa + 156wb + 141wc + 160wd + 157we - 285wf + 111wg > 157 Interns trained 47wa + 3w6+26wc + 21wd + 82we + 92wf + 89wg > 82 ET, wa, wb, wc, wd, we, wl, wg 20 (b) solve the model. (EI, wa, wb, wc, wd, we, wr, wg) - (c) Is hospital E relatively inefficient? Yes No What is the interpretation of the value of the objective function? The value of El indicates that Hospital E requires more resources in order to continue producing at its output level. The value of El indicates that all the resources used by Hospital E are required to produce the outputs of Hospital E. The value of ET indicates that Hospital E should have a surplus of resources, based on its output. (d) Which hospitals are involved in making up the composite hospital? (Select all that apply.) Hospital A O Hospital B Hospital Hospital D Hospital E Hospital F Hospital Can you make a general statement about which hospitals will make up the composite unit associated with a unit that is not inefficient? If a hospital Select relatively inefficient, then-Select- A linear programming computer package is needed. The following data from a particular study involving seven teaching hospitals include three input measures and four output measures. Input Measures Full-Time Supply Bed-Days Hospital Equivalent Expense Available Nonphysicians (1000s) (1000s) 310.0 134.60 116.00 B 278.5 114.30 106.80 165.6 131.30 65.52 D 250.0 16.0 94.40 E 206.4 151.20 102.10 F 384.0 217.00 153.70 G 530.1 770.80 215.00 Output Measures Patient-Days Hospital (65 or older) (1000s) Patient-Days (under 65) (1000s) Nurses Trained Interns Trained $5.31 49.52 291 47 B 37.64 55.63 156 3 32.91 25.77 141 26 D 33.53 41.99 160 21 E 32.48 55.30 157 82 LL 48.78 81.92 285 92 G 58.41 119.70 111 89