Question

a printing company orders paper from two different suppliers. supplier x charges $25 per case. supplier y charges $20 per case. the company needs to order at least 45 cases per day to meet demand and can order no more than 30 cases from supplier x. the company needs no more than 2 times as many cases from supplier y as from supplier x. let x = the number of cases from supplier x and y = the number of cases from supplier y. complete the constraints on the system. y ≤ \boxed{}x x + y ≥ \boxed{} x ≤ \boxed{} done

Explanation:

Step1: Translate Y's limit to inequality

The company needs no more than 2 times as many cases from Supplier Y as from X, so $y \leq 2x$.

Step2: Translate minimum order constraint

The company needs at least 45 cases total, so $x + y \geq 45$.

Step3: Translate X's maximum order constraint

The company can order no more than 30 cases from X, so $x \leq 30$.

Answer:

$y \leq \boldsymbol{2}x$
$x + y \geq \boldsymbol{45}$
$x \leq \boldsymbol{30}$