Suppose the elevator stops at the X floor, and on the first floor, Y goes upstairs directly without taking the elevator. Then the total score of dissatisfaction is s = 3 [1+2+…+(33-x)]+3 (1+2+…+y)+[1+2+…+.
= 2 x2-xy- 102 x+2 y2+3y+ 1684
= 2 x2-(y+ 102)x+2 y2+3y+ 1684
=2*[x-(y+ 102)/4]? + 15/8(y-6)? +3 16
≥3 16 .
When x=27 and y=6, S=3 16.
Therefore, when the elevator stops at the 27th floor, the total score of dissatisfaction is the smallest, and the lowest is 3 16.
(You can even get an equal sign by sorting it out. There is a summation formula, that is, the first term plus the last term multiplied by the number of terms divided by 2. )
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