Case Problem # $3.$ Evaluating Relative Efficiencies ofHospital Decision Making Units$$Data Envelopment Analysis $($DEA$)$ is an application of linear programming used to measure the relative efficiency of operating units with the same goals and objectives. As explained in the course, DEA can measure the relative efficiency of a group of hospitals. The data seen below involving seven teaching hospitals include three input measures and four output measures.

$.$A$-$ formulate a linear programming model so that DEA approach can be used to evaluate the performance of hospital D$.$

b$.$ Solve the problem formulated in $($a$),$ and show all of the Excel or QM templates you use in your formulation.$$

c$.$ Is hospital D relatively inefficient? What is your interpretationof the value of the objective function?$$

d$.$ How many patient$-$days of each type are produced by thecomposite hospital?$$

e$.$ Which hospital would you recommend hospital D consider emulating to improve the efficiency of its operation?