Question

Find the indicated maximum or minimum value of the objective function in the linear programming problem. Maximize f - 30x + 40y subject to the following constraints. x + 2y = 48 x + y s 30 2x + y 50 x 20, y 20 Need Help? Read It Vatch It Talk to a Tutor -/12.5 POINTS HARMATHAP9 4.2.015.MI. EE Solve the following linear programming problem. Restrict x 20 and y 20. Maximize = 3x + 5y sub/ect to the following. x + y S6 2x + y s 10 Y53

Answer 1

Max. f = 30x + 4oy. subject to xit 24 248 aty < 30 2.*+450 x70 yoo Consider al inequalities ou egualities x+2y=48 ty=30 2x+y = 50 The shaded region Now, we find 0(0,0) OABC DO is the feasible region beatest coordinates of comer points A (25,0) 0(0,24)

for E point B page ③ 2x+y =50 - *+4=30 perform - = 2.0) put this in 20+ 230 y = 30-20= 10 For "B(x, y) = B (2010) point c 1+y = 30 +2y = 48 - 6 perform - 6 - y = -18 = 18 put this in equation ③ x+18=30 = x=30-18 = 12 x=12 (12,18) to 30x+404 is objective function 610,0) = 30.0+40.0 = 0 to=0 Now, ta (25,0) = 30.25 +40-0= 750 +0=750 fo(20,10) = 30.10+40.10 = 600+400 =1000 fe (12, 18) = 30,12 +40.18 = 360+720 = 1090 fo (0, 24)=30.0+40 24 = 960 maximum value off is 10g0 at point c(12, 18).

② page Maximize f-34+54. subject to x + y 26 2x + y 210 & 720, 420 all as equalities Consider x+y=6 inequalities 2x+4 = 10 y=3 + -21 Olo 2A4 The shaded Now region region OABCO is feasible we find coordinates of 000,0). A(3,0) @ C(0,6) corner points

page To find coordinates of point B Y-3 fty = 6 x+3=6 x=6-3=3 B(x,y)= B(3,3) f=3x+54 is objective function Jo (0,01= 3.0+5-0=0+0=0 FA(3,0) = 3.3+5.0=9+0=9 fB (33) = 3.3 +5.3=9+15=24 fc (0,6)=3.0+5.6=0+30=30 Marimum value C(0,6) of f is 30 at point