Kelsey is knitting baby items to sell at a craft fair. she has a total of 1,620 yards of yarn to use for the items. a pair of mittens uses 81 yards of yarn and a blanket uses 162 yards. she wants to knit a minimum of 12 items for the fair. if the solution region represents the number of pairs of mittens and blankets that kelsey can knit, determine which graph represents the solution set to the system of inequalities representing this situation.

She has a total of 1,620 yards of yarn to use for the items:
Total yards of yarn: T<=1,620

Number of Pairs of Mittens: x
x>=0, then the feasible region is to the right of the y-axis
 A pair of mittens uses 81 yards of yarn
Yards to use for the total pairs of mittens: 81x

Number of blankets: y
y>=0, then the feasible region is above the x-axis
a blanket uses 162 yards
Yards to use for the total of blankets: 162y

Total yards of yarn: T=Yards to use for the total pairs of mittens + Yards to use for the total of blankets
T=81x+162y
and T<=1,620, then
81x+162y<=1,620
Simplifying this equation dividing all the terrms by 81:
(81x)/81+(162y)/81<=(1,620)/81
x+2y<=20
In this equation, when:
x=0→0+2y<=20→2y<=20→(2y)/2<=(20/2)→y<=10. Point=(x,y)=(0,10)
y=0→x+2(0)<=20→x+0<=20→x<=20. Point=(x,y)=(20,0)
x+2y<=20
The graph of this region is below of the right line that passes through the points (0,10) and (20,0). In the graphs this is the red line.
The second and fourth graph don't apply, because the feasible region in above the red line.

She wants to knit a minimum of 12 items for the fair, then:
x+y>=12
In this equation:
when x=0→0+y>=12→y>=12. Point=(x,y)=(0,12)
when y=0→x+0>=12→x>=12. Point=(x,y)=(12,0)
 x+y>=12
The graph of this region is above of the right line that passes through the points (0,12) and (12,0). In the graphs this is the blue line.
The third graph doesn't apply, because the feasible region in below the blue line.

x>=0, then the feasible region is to the right of the y-axis
y>=0, then the feasible region is above the x-axis
x+2y<=20. The feasible region is below of the red line.
x+y>=12. The feasible region is above the blue line.
The graph with these characteristics is the first graph.

The first graph represents the solution set to the system of inequalities representing this situation.