part a
consider the given system. (look at the picture)
graph the inequalities on your graphing calculator, and find the vertex points of this system.
part b
in part a, you obtained the vertex points of the given system. test these vertex points in the objective function, f(z) = 4x + 6y using a graphing calculator. find the maximum point.

  A. see below for a graph

  B. f(x, y) = f(0, 15) = 90 is the maximum point

Step-by-step explanation:

A. See below for a graph. The vertices are those defined by the second inequality, since it is completely enclosed by the first inequality: (0, 0), (0, 15), (10, 0)

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B. For f(x, y) = 4x +6y, we have ...

  f(0, 0) = 0

  f(0, 15) = 6·15 = 90 . . . . . the maximum point

  f(10, 0) = 4·10 = 40

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Comment on evaluating the objective function

I find it convenient to draw the line f(x, y) = 0 on the graph and then visually choose the vertex point that will put that line as far as possible from the origin. Here, the objective function is less steep than the feasible region boundary, so vertices toward the top of the graph will maximize the objective function.

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step-by-step explanation: