Let x = the number of bags of red beads
Let y = the number of bags of blue beads
A bag containing red beads costs $2 per bag.
A bag containing blue beads costs $3 per bag.
You can spend at most $60 on beads.
The shading will be below this line
Draw the boundary line 2x + 3y = 60 solid.
It has intercepts (0,20) and (30,0)
You need more bags of blue beads
than bags of red beads,
Draw the boundary line y = x dotted.
The shading will be above this dotted line.
a. Write and graph a system of linear inequalities that represents the situation.
b. Identify and interpret a solution of the system.
The set of solutions is the feasible region, which you should
shade. (I can't shade here but you can on your paper).
c. Use the graph to determine whether you can buy 9 bags of red beads and
12 bags of blue beads.
We plot the point (x,y) = (9,12) and see if it falls inside
that triangle.
Yes the point (9,12) is inside the set of solutions, so
you can buy 9 bags of red beads and 12 bags of blue beads.
Edwin