2). At a local hospital, the basic emergency surgical procedures are classified into 4 types. Surgical residents are present around the clock in two 12 hour shifts, and each shift must include a surgeon capable of performing each type of surgery. Hospital rules prevent a resident from serving two shifts. Residents 2 and 3 have been known to throw scalpels at each other and thus cannot work together. The capabilities of the seven residents on staff are given in the table below. Res. 1 Res. 2 Res. 3 Res. 4 Res. 5 Res. 6 Res. 7 yes yes yes yes yes yes Surgical type 1 Surgical type 2 Surgical type 3 Surgical type 4 yes yes yes yes yes yes yes The hospital wishes to assign surgeons to shifts for one 24 hour period minimizing the number of surgeons used. Formulate an integer programming problem. (Do NOT solve - just formulate!)