To determine the constraints for the system based on the given information, let's break down each part of the problem step-by-step:
1. Minimum Order Requirement:
The company needs to order at least 45 cases per day to meet demand. This translates to the constraint:
[tex]\[
x + y \geq 45
\][/tex]
2. Maximum Order from Supplier X:
The company can order no more than 30 cases from Supplier X. This gives us the constraint:
[tex]\[
x \leq 30
\][/tex]
3. Order Proportions between Supplier Y and Supplier X:
The company needs no more than 2 times as many cases from Supplier Y as from Supplier X. This implies:
[tex]\[
y \leq 2x
\][/tex]
Now let's summarize the constraints for the system based on the information given:
- The company needs to order at least 45 cases per day:
[tex]\[
x + y \geq 45
\][/tex]
- The company can order no more than 30 cases from Supplier X:
[tex]\[
x \leq 30
\][/tex]
- The company needs no more than 2 times as many cases from Supplier Y as from Supplier X:
[tex]\[
y \leq 2x
\][/tex]
Therefore, the final constraints on the system are:
[tex]\[
y \leq 2x
\][/tex]
[tex]\[
x + y \geq 45
\][/tex]
[tex]\[
x \leq 30
\][/tex]
Plugging these constraints into the missing spots from the question, we get:
[tex]\[
\begin{array}{l}
y \leq 2x \\
x + y \geq 45
\end{array}
\][/tex]
[tex]\[
x \leq 30
\][/tex]
