IR-32: Shagdarova D. Burkanov A.

max 5x 1 +9x 2 3x 1 +x 2 <=5 5x 1 +x 2 >=15 x 1, x 2 >=0 =>=>=>=> 5x 1 +9x 2 3x 1 +x 2 +S 1 =5 5x 1 +x 2 -S 2 =15 x 1, x 2> =0 S 1,S 2 >=0 max

y i =-x i =>=>=>=> y i >=0 x i <=0 Example: min 5x 1 +9x 2 x 1 +x 2 =5 x 1 <=0 x 2 >=0 =>=>=>=> -5y 1 +9x 2 y 1 +x 2 =5 y 1 >=0 x 2 >=0 min y i =-x i

x j =x i-x i x j>=0 x i>=0 Example: max 5x 1 +9x 2 x 1 +x 2 =5 x 1 >=0 =>=>=>=> max 5x 1 +9x 2- 9x 2 x 1 +x 2-x 2=5 x 1 >=0 x 2>=0

ResourceCake Box of cookies Total available Eggs6430 Time218 Profits10$6$?

X1- # of cakes. X2-# of box of cookies. max 10x 1 +6x 2 S.t. 6x 1 +4x 2 <=30 2x 1 +x 2 <=8 x 1,x 2 >=0 St.f. 6x 1 +4x + S 1 =30 2x 1 +x 2 +S 2 =8 x 1,x 2, S 1, S 2 >=0

X1X2S1S2b X1X2S1S2b /

X1X2S1S2b / negative X1X2S1S2b /

X1 X2 S1 S2 b b / basic v. non-basic v. Opt.value x 1= 1 x 2= 6 S 1, S 2 =0 Optimal solutions 46

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