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Grade 9·8 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-ced-a-3

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Procedures

A meal-planning scenario has two foods: food A ( $10\text{ g}$ protein/lb,
$\text{\char"0024}2$ /lb) and food B ( $5\text{ g}$ protein/lb, $\text{\char"0024}4$ /lb). Let $x$ =
pounds of food A and $y$ = pounds of food B.

Constraints: the meal must provide at least 40 g of protein AND cost at
most $30.

Which system correctly models ALL constraints, including non-negativity?

$10x + 5y \geq 40$
$2x + 4y \leq 30$

$10x + 5y \leq 40$
$2x + 4y \geq 30$
$x \geq 0,\ y \geq 0$

$10x + 5y \geq 40$
$2x + 4y \leq 30$
$x \geq 0,\ y \geq 0$

$10x + 5y = 40$
$2x + 4y = 30$
$x \geq 0,\ y \geq 0$