In order to represent the given scenario using a system of linear inequalities, let's break down the information step by step:
1. Cost Constraints:
- The cost of steak per pound is \(\$4.45\).
- The cost of shrimp per pound is \(\$11.00\).
- The total budget for steak and shrimp is at most \(\$200\).
Therefore, the total cost equation is:
[tex]\[
4.45x + 11y \leq 200
\][/tex]
2. Minimum Steak Requirement:
- You must buy at least 12 pounds of steak.
This can be represented as:
[tex]\[
x \geq 12
\][/tex]
Combining these two constraints, we get the system of linear inequalities:
[tex]\[
\begin{cases}
4.45x + 11y \leq 200\\
x \geq 12
\end{cases}
\][/tex]
This system ensures that the total cost of steak and shrimp does not exceed \(\$200\) and that at least 12 pounds of steak are purchased.
Therefore, the correct option is:
[tex]\[
4.45x + 11y \leq 200 \quad \text{and} \quad x \geq 12
\][/tex]
