Question

Solve by graphical method :

Max
S.t.

Z = 4x + 9y
10x + 5y = 9
3x + 2y = 8
x, y 2 0.​

Answer 1

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Answer 2

The maximum of z is 36 at x=0 and y=4

Step-by-step explanation:

Optimization function, z = 4x + 9y

Constraint equation:

$10x+5y\geq 9$

$3x+2y\leq 8$

$x,y\geq 0$

First draw the graph of constrain and then find z each corner value of feasible region.

Equation 1: 10x + 5y = 9

  x  :  0.9    0

  y  :    0     1.8

Text point: (0,0)

$10(0)+5(0)\geq 9$

$0\geq 9$

False, shade away from origin

Equation 2: 3x + 2y = 8

  x  :  0    2

  y  :  4     1

Text point: (0,0)

$3(0)+2(0)\leq 8$

$0\leq 8$

TRUE, shade towards origin

Common shaded region is feasible region.

$x,y\geq 0$ region should be on first quadrant.

Please find attachment for graph.

At point A(0,4)

z(0,4) = 4(0) + 9(4) = 36

At point B(0,1.8)

z(0,1.8) = 4(0) + 9(1.8) = 16.2

At point C(0.9,4)

z(0.9,0) = 4(0.9) + 9(0) = 3.6

At point D(8/3,0)

z(8/3,0) = 4(8/3) + 9(0) = 10.67

$Z_{max}=36$

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