In linear programming the vertices represent the potential maximums and minimums

Question

In linear programming the vertices represent the potential maximums and minimums for the objective. But what do the boundary lines of the shaded region represent? And what do the points within the shaded region represent? Re-examine the problem below, which is from a previous Lesson, and answer the following questions:
The Mountain Trail Wood Fabricators make wooden tables and chairs. They have 120 man-hours of labor available per week. A table takes 15 man-hours to build and a chair takes 7 man-hours to build. The company warehouse can store 200 board feet of wood. The warehouse is restocked once per week. A table takes 32 board feet of materials to build, and a chair takes 8 board feet of materials to build. The company’s objective is to produce tables and chairs.

This situation can be represented by the following system of inequalities,
15x + 7y = 120, 32x + 8y = 200, x = 0, y =0

and the graph below:
x = the number of tables
y = the number of chairs


Consider the cutout below, which represents the entire solution set for the system of inequalities above:


1. What do the points along the boundary line labeled A represent?

Explanation / Answer

Without seeing which side is labeled A, an answer cannot be given. In fact, your equations show inequality whatsoever but rather they ARE the boundary. I can tell that the "cutout below" consists of shaded region bounded by the x-axis, y-axis, and two lines with different slopes. So, which line is labeled A?

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