Question

find the maximum value of
p = 9x + 8y
subject to the following constraints:
first, identify the y-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 y-intercept formula

To find the y-intercept of a linear equation \(Ax + By = C\), set \(x = 0\) and solve for \(y\). The first inequality is \(8x + 6y \leq 48\), so we consider the boundary line \(8x + 6y = 48\).

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

Substitute \(x = 0\) into \(8x + 6y = 48\):
\(8(0) + 6y = 48\)
Simplify: \(6y = 48\)

Step3: Solve for \(y\)

Divide both sides by 6: \(y=\frac{48}{6}=8\)

Answer:

The y - intercept of the first inequality is 8.