Question

June has decided to take up quilting. She bought a sewing machine for $135. It costs her $11.75 in raw materials to make a quilt, and she can sell a quilt for $28.50.
Which of the following graphs best illustrates June’s situation?
I.A graph has quilts on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 135) and (3, 170). The revenue line goes through (3.5, 100) and (8, 230). The lines intersect at (8, 230). II.A graph has quilts on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 135) and (3, 220). The revenue line goes through (8.5, 100) and (12, 140). III.A graph has quilts on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 135) and (3, 170). The revenue line goes through (0, 135) and (2, 190). The lines intersect at (0, 135). IV.A graph has quilts on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 135) and (3, 100). The revenue line goes through (2.5, 80) and (3, 100). The lines intersect at (3, 100).
a.
I
b.
II
c.
III
d.
IV

Answer 1

Answer: a. I

Reason: Cost C(q) = 135 + 11.75q, revenue R(q) = 28.50q. So C(0)=135 and C(3)=135+3(11.75)=170.25 (≈170), and R(3.5)=3.5(28.5)=99.75 (≈100), R(8)=8(28.5)=228 (≈230). The break-even solves 135+11.75q=28.5q → q≈8.06, y≈229.7. These values match graph I.