Question

find the maximum value of p = 9x + 8y subject to the following constraints: now, identify the x-intercept of the first inequality. \\(\

$$\begin{cases}8x + 6y \\leq 48 \\\\ 7x + 7y \\leq 49 \\\\ x \\geq 0 \\\\ y \\geq 0\\end{cases}$$

\\)

Explanation:

Step1: Recall x-intercept definition

The x - intercept of a line is the point where \(y = 0\). For the first inequality \(8x+6y\leq48\), we consider the boundary line \(8x + 6y=48\) (since the x - intercept of the inequality's boundary line will be the same as the x - intercept relevant for the inequality in terms of the graph).

Step2: Set \(y = 0\) in the boundary line equation

Substitute \(y = 0\) into \(8x+6y = 48\). We get the equation \(8x+6(0)=48\), which simplifies to \(8x=48\).

Step3: Solve for \(x\)

To solve for \(x\), divide both sides of the equation \(8x = 48\) by 8. So \(x=\frac{48}{8}=6\).

Answer:

The x - intercept of the first inequality is 6.