The tollbooth staffing problem

min x1+x2+x3+x4+x5+x6+x7+x8+x9+x10
   +x11+x12+x13+x14+x15+x16+x17+x18+x19
   +x20+x21+x22+x23+x24
subject to
  12:00am)  x1+x17+x18+x19+x20+x22+x23+x24 > 2
   1:00am)  x1+ x2+x18+x19+x20+x21+x23+x24 > 2
   2:00am)  x1+ x2+ x3+x19+x20+x21+x22+x24 > 2
   3:00am)  x1+ x2+ x3+ x4+x20+x21+x22+x23 > 2
   4:00am)  x2+ x3+ x4+ x5+x21+x22+x23+x24 > 2
   5:00am)  x1+ x3+ x4+ x5+ x6+x22+x23+x24 > 2
   6:00am)  x1+ x2+ x4+ x5+ x6+ x7+x23+x24 > 8
   7:00am)  x1+ x2+ x3+ x5+ x6+ x7+ x8+x24 > 8
   8:00am)  x1+ x2+ x3+ x4+ x6+ x7+ x8+ x9 > 8
   9:00am)  x2+ x3+ x4+ x5+ x7+ x8+ x9+x10 > 8
  10:00am)  x3+ x4+ x5+ x6+ x8+ x9+x10+x11 > 4
  11:00am)  x4+ x5+ x6+ x7+ x9+x10+x11+x12 > 4
  12:00pm)  x5+ x6+ x7+ x8+x10+x11+x12+x13 > 3
   1:00pm)  x6+ x7+ x8+ x9+x11+x12+x13+x14 > 3
   2:00pm)  x7+ x8+ x9+x10+x12+x13+x14+x15 > 3
   3:00pm)  x8+ x9+x10+x11+x13+x14+x15+x16 > 3
   4:00pm)  x9+x10+x11+x12+x14+x15+x16+x17 > 6
   5:00pm) x10+x11+x12+x13+x15+x16+x17+x18 > 6
   6:00pm) x11+x12+x13+x14+x16+x17+x18+x19 > 5
   7:00pm) x12+x13+x14+x15+x17+x18+x19+x20 > 5
   8:00pm) x13+x14+x15+x16+x18+x19+x20+x21 > 5
   9:00pm) x14+x15+x16+x17+x19+x20+x21+x22 > 5
  10:00pm) x15+x16+x17+x18+x20+x21+x22+x23 > 3
  11:00pm) x16+x17+x18+x19+x21+x22+x23+x24 > 3
end