Question

Instructions: Given the following constraints, find the maximum and minimum values for z.
x + 3y < 0
Constraints: X – Y > 0
3x – 7y < 16
Optimization Equation: 2 = -x + 5y
Maximum Value of z:
Minimum Value of z:
Check

Answer 1

Answer:

$x+3y\leq 0$        

$x-y\geq 0$

$1) x+3y=0$

$x-y=0$

$-----$

$4y=0$

$y=0$

$x=0$

$(0,0)$

$2)(x+3y=0)3$

$3x-7y=16$

$3x+9y=0$

$3x-7y=16\\------\\16y=-16$

$y=-1$

$(3,-1)$

$3)(x-y=0)3$

$3x-7y=16$

$3x-3y=16$

$3x-3y=0$

$3x-7y=16\\------\\4y=-16$

$y=-4$

$x=4$

$(4,-4)$

$Z=-x+5y$

$(0,0):z=0$

$(3,-1):z=-8$

$(4,-4):z=-24$

$Maximum \:Value\: of\: z:0$

$Minimum\: Value\: of\: z:-24$

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