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If-3-x-4-2-y-5-4-z-10-find-the-greatest-value-of-w-z-xy-

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Question Number 97438 by john santu last updated on 08/Jun/20
If −3≤x≤4, −2≤y≤5, 4≤z≤10 , find the greatest value of w = z−xy
If−3⩽x⩽4,−2⩽y⩽5,4⩽z⩽10,findthegreatestvalueofw=z−xy
Commented by bemath last updated on 08/Jun/20
for xy = −15 and z = 10 then max of w = z−xy = 10−(−15)=25
forxy=−15andz=10thenmaxofw=z−xy=10−(−15)=25
Answered by 1549442205 last updated on 08/Jun/20
From the hypothesis { ((−3≤x≤4)),((−2≤y≤5)) :} we get 20≥xy≥−15⇒−20≤−xy≤15(1)which by the combine to 4≤z≤10 (2),plus two same dimension inequalities (1)and (2) we obtain that −16≤z−xy≤25.This means z−xy_(min) =−16 when (x;y;z)=(4;5;4)and z−xy_(max) =25 when (x;y;z)=(−3;5;10)
Fromthehypothesis{−3⩽x⩽4−2⩽y⩽5weget20⩾xy⩾−15⇒−20⩽−xy⩽15(1)whichbythecombineto4⩽z⩽10(2),plustwosamedimensioninequalities(1)and(2)weobtainthat−16⩽z−xy⩽25.Thismeansz−xymin=−16when(x;y;z)=(4;5;4)andz−xymax=25when(x;y;z)=(−3;5;10)

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