Question

find the maximum value of
p = 9x + 8y
subject to the following constraints:
now, identify the y-intercept of the second 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 \(Ax + By = C\), we set \(x = 0\) and solve for \(y\). The second inequality is \(7x+7y\leq49\). We consider the boundary line \(7x + 7y=49\) (since the y - intercept of the inequality will be the same as the y - intercept of its boundary line).

Step2: Substitute \(x = 0\) into the boundary line equation

Substitute \(x = 0\) into \(7x+7y = 49\). We get \(7(0)+7y=49\), which simplifies to \(7y = 49\).

Step3: Solve for \(y\)

Divide both sides of the equation \(7y = 49\) by 7. So, \(y=\frac{49}{7}=7\).

Answer:

The y - intercept of the second inequality \(7x + 7y\leq49\) is 7.