Question: The Stone Company produces three sizes of window fans: small, medium, and The manager has formulated an LP model for fan production:

maximize \(\quad 6 x_{1}+8 x_{2}+5 x_{3} \quad\) (profit)

subject to

\(\begin{aligned} \text { Labor } & 3 x_{1}+4 x_{2}+5 x_{3} & \leq 160 \text { hours } \\ \text { Metal } & 1 x_{1}+2 x_{2}+3 x_{3} & \leq 100 \text { pounds } \\ \text { Plastic } & 2 x_{1}+2 x_{2}+2 x_{3} & \leq 110 \text { pounds } \\ \text { Large fan } & x_{3} & \geq 18 \\ x_{1}, x_{2}, x_{3} & \geq 0 \end{aligned}\)

Briefly explain or define each of these parts of the model:

1. \(\quad x_{1}, x_{2}\), and \(x_{3}\).
2. The 6 in the objective function.
3. The product of the 8 and \(x_{2}\) in the objective function.
4. The terms labor, metal, and plastic.
5. The 5 in the labor constraint.
6. The 160 hours.
7. \(\quad x_{3} \geq 18\)
8. The product of 5 and \(x_{3}\) in the labor constraint.
9. \(\quad x_{1}, x_{2}, x_{3} \geq 0\)
10. What two key questions can be answered using this model?

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