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) A 310.0 134.60 116.00 B 278.5 114.30 106.80 165.6 131.30 65.52 D 250.0 316.00 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 Patient-Days Hospital (65 or older) (under 65) (1000s) (1000s) Nurses Trained Interns Trained A 55.31 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 F 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 El = the efficiency index.) Min s.t. sum weights Full-time equivalent nonphysicians Supply expenses ($1,000s) Bed-days available (1,000s) Patient-days (65 or older) (1,000s) Patient-days (under 65) (1,000s) Nurses trained Interns trained EI, wa, wb, wc, wd, we, wf, wg > 0 (b) Solve the model. (EI, wa, wb, wc, wd, we, wf, 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 all the resources used by Hospital E are required to produce the outputs of Hospital E. The value of er indicates that Hospital E should have a surplus of resources, based on its output. The value of EI indicates that Hospital E requires more resources in order to continue producing at its output level (d) Which hospitals are involved in making up the composite hospital? (Select all that apply.) Hospital A Hospital B Hospital Hospital D Hospital E Hospital F Hospital G 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