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The first line passes through the origin and the point left parenthesis 8 comma 8 right parenthesis.

The second line passes through the y-axis at 6 and the point left parenthesis 4 comma 4 right parenthesis.
The third line is horizontal through the y-axis at 8.
The region to the left of the first line, above the second line, below the horizontal line and right of the y-axis is shaded.    Question 3 Equation

What is the minimum value for z equals 3 x minus one-half y over the feasibility region defined by the constraints shown above?

boundary lines:
y = 8
y = x
y = -1/2 x + 6

critical points, such as intersections:
(0,6), (4,4), (8,8), (0,8)

z = 3x - 1/2

none of the critical points will yield a z value of -8