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 overall equation represented by this scenario? (all points may not apply to the scenario.)

Explanation:

Step1: Define total items equation

Each pair of pillows is $y$, so total pillows are $2y$. Total items: $x + 2y \geq 4$

Step2: Rewrite to slope-intercept form

Rearrange: $2y \geq -x + 4$ → $y \geq -\frac{1}{2}x + 2$

Step3: Analyze graph properties

• Boundary line: $y = -\frac{1}{2}x + 2$, crosses $x$-axis at $(4,0)$, $y$-axis at $(0,2)$.
• Inequality $\geq$ means solid line, shaded above the line.
• Non-negative values for $x,y$ (can't order negative items).

Answer:

The second graph (middle one: solid line $y = -\frac{1}{2}x + 2$, shaded region above/left of the line covering non-negative $x,y$ values)