Question

Find the maximum and minimum of P = 16x + 15y subject to: OSX 10 Osys5 3x + 2y 2 6. 160,45 235, 160 235.45 75.45

Answer 1

P=164+15y. To find! The maximum and minimum of subject to osusio 03435 3x+2y=6 The point of intersection of 3ut2y=6 and the x-axis is A(2,0) • The point of intersection of x=10 and the x-axis is B(10,0) The point of intersection of n=10 and y=5 is c(105) o The point of intersection of y=5 and the y-axis is D(05) • The point of intersection of 3ut2y = 6 and the yaxis is E(0, 3) The feasible region is as shown in the graph, whose corner points are A(2,0), B(100), 2(10,5), D10,5), ECO3) The objective function is P = 16utisy At A (2,0), P=16(2) +1560) = 32+0 = 32 At B(190), P=16(10)+15(0) = 160+0=160 At c( 10,5), P=16110)+15(5)= 160+75=235 At D(0,5), P=16(0)+1565)=0+75=75 At E(0,3), P = 16(0)+15(3)=0+ 452 45 The maximum of P - 235 The mini of P = 32 mym

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