HW $5($Ch $5$ Advanced LP$)\backslash$table$[[,,\backslash$table$[[$Input$],[$Measures$]],],[$Hospital$,\backslash$table$[[$Full$-$Time$],[$Equivalent$],[$Nonphysicians$]],\backslash$table$[[$Supply$],[$Expense$],[(1000$s$)]],\backslash$table$[[$Bed$-$Days$],[$Available$],[(1000$s$)]]],[$A$,310\mathrm{.}0,134\mathrm{.}60,116\mathrm{.}00],[$B$,278\mathrm{.}5,114\mathrm{.}30,106\mathrm{.}80],[$C$,165\mathrm{.}6,131\mathrm{.}30,65\mathrm{.}52],[$D$,250\mathrm{.}0,316\mathrm{.}00,94\mathrm{.}40],[$E$,206\mathrm{.}4,151\mathrm{.}20,102\mathrm{.}10],[$F$,384\mathrm{.}0,217\mathrm{.}00,153\mathrm{.}70],[$G$,530\mathrm{.}1,770\mathrm{.}80,215\mathrm{.}00]]\backslash$table$[[$Hospital$,\backslash$table$[[$Patient$-],[$Days $(65],[$or older$)],[(1000$s$)]],$Output Measures,$\backslash$table$[[$Interns$],[$Trained$]]],[\backslash$table$[[$Patient$-],[$Days$],[($under$],[65)],[(1000$s$)]],\backslash$table$[[$Nurses$],[$Trained$]]],[$A$,55\mathrm{.}31,49\mathrm{.}52,291,47],[$B$,37\mathrm{.}64,55\mathrm{.}63,156,3],[$C$,32\mathrm{.}91,25\mathrm{.}77,141,26],[$D$,33\mathrm{.}53,41\mathrm{.}99,160,21],[$E$,32\mathrm{.}48,55\mathrm{.}30,157,82],[$F$,48\mathrm{.}78,81\mathrm{.}92,285,92],[$G$,58\mathrm{.}41,119\mathrm{.}70,111,89]]$ d$.$ How many patient$-$days of each type are produced by the composite hospital?

e$.$ Which hospitals would you recommend hospital D consider emulating to

improve the efficiency of its operation?

Answer the following three problems:

$(1)$ Problem $4($DEA$)$

Hospital Efficiency. Data envelopment analysis can measure the relative efficiency

of a group of hospitals. The following data from a particular study involving seven

teaching hospitals include three input measures and four output measures. LO$1$

a$.$ Formulate a linear programming model so that data envelopment analysis can

be used to evaluate the performance of hospital D$.$

b$.$ Solve the model.

c$.$ Is hospital D relatively inefficient? What is the interpretation of the value of

the objective function?