Problem $2.$ A hospital outpatient clinic performs four types of operations. The profit per

operation, as well as the minutes of X$-$ray time and laboratory time used, are given in the

table below. The clinic has $500$ private rooms and $500$ intensive care rooms. Type $1$ and

type $2$ operations require a patient to stay in an intensive care room for one day, whereas

type $3$ and type $4$ operations require a patient to stay in a private room for one day. Each

day, the hospital is required to perform at least $100$ operations of each type. The hospital

has set the following goals $($listed in order of priority$)$: