subject: Math

solve the following questions ( handwritten solution only neatly and clean box final answer) thankyou!

solution must be same as the sample below

ST. MARY'S COLLEGE TAGUM, INC. GRADUATE EDUCATION PROGRAM National Highway, Magugpo East, Tagum City. 810p Norte, Philippines Quality Transformative Ign Marian Education MATHEMATICS INVESTIGATION GROUP M103 - Applied Mathematics Second Semester, Second Term S.Y. 2023-2024 1. Maximize z = 3x + 7y subject to 3x - 2ys7 2x + 5ys6 2x + 3ys8 x20, y20 2. Maximize z = 2x, + 3x,, - 4x, subject to 3x, - 2x, +x 54 2x, + 4x, + 5x,56 x, 20, x,20, x,20 3. Maximize z = 2x, + 2x, + 3x,+ x, subject to 3x, - 2x, +x, +x 56 x, +x, +x,+x58 2x, - 3x, - x, + 2x $10 x, 20, x,20, x, 20 , x 20Maximize : 2: 4 x , + 8 x2 + 5x3 Slack Variables Subject to 1 X 1 + 2 x 2 + 3 * = =18 OX4, OXs , 0Xp 3 2 X,+6*2 + 4x3615 X 1 2 X 2 , X, 20 2 = 4X , +8*2+ 5X3-0X4 -0x 5- 0X4 Maximize (of ) - 4 x, - 8X2 - 5X &tox+ toxs +oxy D X , + 2 x 2 + 3 *3 + X+ = 18 (2 X , + 4 * 2 + X3+X5= 6 3 2 X 1 + 4 X 2 + 4 *3 +X 6= 15 XisXz ,X3,*5 20 Obicitive function X z X3 X4 XS O I b rabo Basis - 4 5 O 1 1 2 3 O 0 141 1: 2 09 RI 0 64 7/ 2 ) Rz (X5- X2: 41 5 / 2 2 4 O X - OXI Xz X3 XF XC *6 2 b ration OKF - 2 0 -3 O 2 O 1 12 KIXA 1/2 O 5 /2 1 - 1/2 O 0 15 6 1/4 1 1/ 4 0 0 3/ 2 0 3/2 6 Ra X6 - Xq 1/2 0 5 / 2 5 -3 2 O 2.4 Rzold : 4 = R. new D Rgold - 6 RX new = Ry new RJ old - 2R2 new = Rinew ORFold + 8RX New= new ORF (X. X z X 3 2 b rah o OFR - 715 115 e /s 1 O O 2/5 9 / 10 9 12 12 X2 - XX, I O O - 315 O 12 / 12 0 Ly Forus old R 3 x ( 2 / 5 ) = Rx new R2 Old - 1/4 Rynew = R2 new RI old - 5 /2 Rg new = Kinew JOCK+ multiply by 31 8 XI Xz Si Sz R2 old - 2/0 R, mew Basis CB 7 4 0 0 6 = R2 new X2 64/0 1 3/8-14 3 10 1 1- 2/2 ( 0 ) = 1 X1 72 1 0 - 14 1/2 2 V 2/2- 2/3 (1 ) = 0 0- 2/3 ( 7/83) = - 1/4 * 2 + x i j z 7 6 1 /2 2 ( 2) Z 1/3- 2/3( - ' /4 ) = 1 /2 cj - 2;160 - 1/2- 2 4- 2/3 (2 ) = 2 optimal solution x 1 = 2, X z = 3, 51 = 0, 52= 0, 2= 32