Question

1 a local restaurant owner can purchase tea for $16 per pound and coffee for $8 per pound. his budget does not allow him to spend more than $280 on coffee and tea. which graph shows the possible combinations of pounds of tea, x, and pounds of coffee, y, that the restaurant owner can purchase? a graph a, b graph b, c graph c, d graph d

Explanation:

Step1: Build budget constraint equation

Let $x$ = pounds of tea, $y$ = pounds of coffee.
The total cost is $16x + 8y \leq 280$.
Simplify: divide by 8: $2x + y \leq 35$, or $y \leq -2x + 35$.

Step2: Find x-intercept (y=0)

Set $y=0$, solve for $x$:
$2x + 0 = 35 \implies x = \frac{35}{2} = 17.5 \approx 18$

Step3: Find y-intercept (x=0)

Set $x=0$, solve for $y$:
$0 + y = 35 \implies y = 35$

Step4: Match intercepts to graphs

The line has a y-intercept of 35 and x-intercept of ~18, which matches Graph B.

Answer:

B