一栋n层大楼,各层均可召集n个人开会,现每层指定一人到第k层开会,为使n位开会人员上下楼梯所走路程总和最短,则k应取( )
A.
n
B. n为奇数时,k=
(n+1),n为偶数时k=
n或
n+1
C.
(n+1)
D. n为奇数时,k=
(n-1),n为偶数时k=
n
设每走一层楼梯的路程为a,n位开会人员上下楼梯所走路程总和为S,则S=a(1+2+…+k-1)+0+a[1+2+…+(n-k)]=a•(k−1)•k2+a•(n−k)•(n−k+1)2=a[k2−(n+1)k+12(n2+n)]∵二次函数F(k)=k2−(n+1)k+12(n2+n)图象关...