Question

A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the possible combinations of sofa and pillow orders the manager can have?

Answer 1

Answer: D

Step-by-step explanation:

Answer 2

Answer:

• It is the last graph: solid line, shaded area over the line x = 2 - x/2

Explanation:

1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:

• Number of sofas: x (given)
• Number of pillows: 2y (given, since they come in pairs)
• Number of items = number of sofas + number of pillows = x + 2y
• Minimum of 4 items in each order (given) ⇒ x + 2y ≥ 4

2) Predict the graph of the inequality x + 2y ≥ 4

• The border line is the equation x + 2y = 4
• You can choose two points to draw a line
• Choose the axis-intercepst:

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

• The shading area is above the line because when you solve for y you get y ≥   2 - x/2, and the line is included because the "equal to" part of the symbol (≥ means greater than or equal to).

•  To state that the line is included the graph uses a continous line instead of a dotted one.

3) Conclusion:

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.