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Question 4

Your company is catering an employee lunch. The client has ordered both steak and shrimp. Steak costs [tex]\[tex]$ 4.45[/tex] per pound, and shrimp costs [tex]\$[/tex] 11[/tex] per pound. You can spend no more than [tex]\$ 200[/tex] on these items, and you must buy at least 12 pounds of steak. Let [tex]x[/tex] be the number of pounds of steak and [tex]y[/tex] be the number of pounds of shrimp.

Which system of linear inequalities represents this scenario?

A.
[tex]\[
\begin{cases}
4.45x + 11y \leq 200 \\
x \geq 12
\end{cases}
\][/tex]

B.
[tex]\[
\begin{cases}
4.45x + 11y \leq 200 \\
x \geq 12
\end{cases}
\][/tex]

C.
[tex]\[
\begin{cases}
4.45z + 11y \ \textgreater \ 200 \\
c \ \textless \ 12
\end{cases}
\][/tex]

D.
[tex]\[
\begin{cases}
z + 11y \leq 200 \\
4.45x \geq 12
\end{cases}
\][/tex]



Answer :

GinnyAnswer
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]