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A printing company orders paper from two different suppliers. Supplier [tex]$X$[/tex] charges \[tex]$25 per case. Supplier $[/tex]Y[tex]$ 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
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]
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