Question

Solve the linear programming problem.

Minimize and maximize

z=50x+10y

Subject to	2x+y	≥	32
	x+y	≥	24
	x+2y	≥	28
	x, y	≥	0

Answer 1

solution: The provided informations in the question Minimize and maximize z=soxt loy subject to ozxty 732 x+y 7,24 XARY 7,28 X,7 7,0 The above problem some graphical method. Poltroz Minimize z=50xHoy subject to 2%A77,32 xty 7,24 Xt247128 co-ordinate A lines 2x+y=32 Cusio (16,0), (0,32 ) X+7=24 (24,0) 10124) x+2y = 28 24 22152 Ecommons 4 8 12 16 20 29 28 32 2x+1=32 xty=24

Co-ordinates (0,32) (08, 16) (20, 4) value alor=So&tloy! 320 560 1040 1600 Hence Tminz-320) at 10,32) optromum solutky x = qara soxtoy sub to 2x+4 732 xty 24 Xtzy 7,28 Xi7 7o co-ordinates of lines axty 732 (16,0), (0,32) Xty=24 E O (24,0), (0,24) X+2y =28 (28,0) (0,14) 1-24 of op my - 8 12 16 20 24 28 32

co-ordmats (a, 32) C, 160 (2o, a (28, o) value (z=50x + loy) 320 560 Joho 14oo Hence Tax z=14oo optimum solutzn at (28, o x=28, y=o .