X≥1 x≤7 y≥-1/3x+6
which graph best represents the feasibility region for the system shown above?

The feasible region for the system is shown below.

Step-by-step explanation:

The given system of inequality is shown below,

The related equation of first two inequalities are x=1 and x=7 respectively. Both are vertical lines solid lines because the points on the lines are included in the solution set.

The first inequality is , so shade the area to the right.

The second inequality is , so shade the area to the left.

The related equation of third inequality is

Here, the slope of the line is -1/3 and y-intercept is 6.

At x=3,

Plot these two points (0,6) and (3,5) on the coordinate plane and connect them by a straight line.

Check the inequality by (0,0).

This statements is false. It means (0,0) is not included in the shaded region of third inequality.

So, shade the area above the related line and related line is a solid line because the sign of inequality is ≥.

Therefore, the common shaded region represents the feasibility region.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet