URGENT!! HELP PLEASE!!
Linear programming problems can also be solved using a graphing calculator. The following instructions will work for most commonly used graphing calculators, but note that they might vary slightly based on calculator model. Now that you’ve learned how to use a graphing calculator to solve linear programming problems, solve the following problems.
Part A
Consider the given system
{2x+y ≤20
{3x+2y ≤30
{x,y ≥0
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. 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.