Question

Which conditions on a and b will ensure that the maximum value of P occurs at C? The corner points for the bounded feasible region determined by the system of inequalities shown below are 0 = (0,0), A=(0,7), B = (2,6), and C=(4,0). x+2y = 14 3x + y s 12 X, y = 0 I P = ax + by and a, b>0, determine conditions on a and b that will ensure that the maximum value of P occurs only at C O A. b=3a B. <<3 <b<3a Ос, b> За OD b=2 O E. a = 36 OF. b 2 sa 36 OG OH. a> 3b b</ of OL NO NI OJ. b asz of

Answer 1

We are given the corner points of the bounded feasible region, bounded by given insequalities. And corner points are 0=0,0), A = (0,7), B=(2,6), c=(4,0). Ginien po = ax+by i 9,60, :: P(0) = P(0,0)=0; P(A) = P(0.7) = 7+; PCB) = P1246) = 20+60; PCC)= P(410) Then maximum value of P occur at only c if awe have: = 49

PCC) > max {P(O), PA), PB) } P(C) = 40 > maxdo, 76, 29 +6+} die. PCC) -( I > 40> mar ļ76, 20+66}

esepression, 4a > 76 and 49 > 20+66. ay 4 and 2a > 6 6 Zb a 7 1 4 and a>36 367 > 2 - 6 la>3b b>0. which ensure This is the required condition for a&b that the maximum value of p occur at C. {
so H is the correct option.