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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: z = -x + 5y
Maximum Value of z: 0
Minimum Value of z:

Instructions Given the following constraints find the maximum and minimum values for z x 3y lt 0 Constraints x y 0 3x 7y lt 16 Optimization Equation z x 5y Maxi class=

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Answer:

The answer is below

Step-by-step explanation:

Given the constraints:

x + 3y≤ 0; x - y ≥ 0 and 3x - 7y ≤ 16.

We have to first plot the constraints using the geogebra online graphing tool. Plotting the constraints gives the solution as:

A(0, 0), B(3, -1) and C(-4, -4).

Next using the optimization equation: z = -x + 5y

At point A(0, 0); z = -0 + 5(0) = 0

At point B(3, -1); z = -3 + 5(-1) = -8

At point C(-4, -4); z = -4 + 5(-4) = -24

Hence the maximum value of Z is 0 and the minimum value of Z is -24.

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