A hospital employs volunteers to staff the reception desk between $8$:$00$ a$.$m$.$ and $6$:$00$ p$.$m$.$ Each volunteer works three consecutive hours. The minimum need for volunteers is approximated by a step function over $2-$hour intervals starting at $8$:$00$ a$.$m$.$ as $8,5,7,6,$ and $4.$ Because most volunteers are retired individuals, they are willing to offer their services at any hour of the day $(8$:$00$ a$.$m$.$ to $6$:$00$ p$.$m$.).$ However, because of the large number of charities competing for their service, the number needed must be kept as low as possible. Formulate as an LP problem.