Question

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

To find the x-intercept, set \( y = 0 \) in the second inequality \( 7x + 7y \leq 49 \).

Step2: Substitute \( y = 0 \) into the inequality

Substitute \( y = 0 \) into \( 7x + 7y = 49 \) (we consider the equality for finding the intercept):
\( 7x + 7(0) = 49 \)
Simplify: \( 7x = 49 \)

Step3: Solve for \( x \)

Divide both sides by 7: \( x=\frac{49}{7}=7 \)

Answer:

7