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

`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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