Question $1$

Optimal Solution $-$ Part I: The optimal solution is to:

Use $11\mathrm{.}67$ Hours of Labor, $23\mathrm{.}33$ Board$-$Feet of Wood, and $35$ Hours of Machine Time.

Make $25$ Tables, $5$ Chairs, and $0$ Bookcases.

Make $0$ Tables, $0$ Chairs, and $11\mathrm{.}67$ Bookcases.

Use $55$ Hours of Labor, $400$ Board$-$Feet of Wood, and $35$ Hours of Machine Time.