Question

Which graph is the correct shaded in the graph for the inequality provided?

Answer 1

It is helpful to know several forms of the equation of a line. One that is often overlooked is the intercept form.
.. x/(x-intercept) +y/(y-intercept) = 1

The boundary conditions for your inequalities can be written as the lines
.. x/20 +y/20 = 1
.. x/24 +y/15 = 1

The first inequality will be bounded by the line that has x=20 and y=20 as its x- and y-intercepts. The second inequality will be bounded by the line with x=24 and y=15 as its x- and y-intercepts. Since the inequality conditions include the "or equal to" case, the graphed boundary line will be solid, not dashed. (All but the first graph have these lines properly shown.)

The region shaded for each inequality will be the half-plane (or its portion in the first quadrant) where the x- and y-values make the inequality true. For this problem, that is values of x and y to the left/below the line in both cases. Graph (c) shows where these "feasible regions" overlap, so is the correct choice.