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A printing company orders paper from two different suppliers. Supplier [tex]\( X \)[/tex] charges \[tex]$25 per case. Supplier \( Y \) charges \$[/tex]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 [tex]\( X \)[/tex]. The company needs no more than 2 times as many cases from Supplier [tex]\( Y \)[/tex] as from Supplier [tex]\( X \)[/tex]. Let [tex]\( x \)[/tex] be the number of cases from Supplier [tex]\( X \)[/tex] and [tex]\( y \)[/tex] be the number of cases from Supplier [tex]\( Y \)[/tex].

Complete the constraints on the system:

[tex]\[
\begin{array}{l}
y \leq 2x \\
x + y \geq 45 \\
x \leq 30
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's construct the required constraints based on the details provided:

1. No more than 2 times as many cases from Supplier Y as from Supplier X: This constraint can be expressed as:
[tex]\[ y \leq 2x \][/tex]
Here, the coefficient is [tex]\(2\)[/tex].

2. Total number of cases from both suppliers must be at least 45: This constraint can be expressed as:
[tex]\[ x + y \geq 45 \][/tex]

3. No more than 30 cases from Supplier X: This constraint can be expressed as:
[tex]\[ x \leq 30 \][/tex]

Summarizing all constraints, we get:
[tex]\[ \begin{array}{l} y \leq 2x \\ x + y \geq 45 \\ x \leq 30 \end{array} \][/tex]

Hence, the constraints are:
1. [tex]\( y \leq 2x \)[/tex]
2. [tex]\( x + y \geq 45 \)[/tex]
3. [tex]\( x \leq 30 \)[/tex]
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