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]
