The objective function in this problem is to maximize the economic gain, which is the total profit from producing tables and chairs. Given the profits:

• Each table (T) generates a profit of $120.
• Each chair (C) generates a profit of $80.

The objective function should maximize the total profit from producing $T$ tables and $C$ chairs. Therefore, the objective function is:

$\text{Maximize } 120T + 80C$

Thus, the correct answer is:

b. Maximize $120T + 80C$

Would you like to proceed with defining constraints, or do you have any questions about this step?

Here are some related questions to explore:

1. How would you define the constraints based on the available hours for each stage?
2. What would happen if the profit per table or chair changed?
3. How would the production schedule change if more hours were available for inspection?
4. Can we solve for $T$ and $C$ to maximize profit given the constraints?
5. How would the objective function change if there was a penalty for unutilized hours?

Tip: In linear programming, the objective function is always set to either maximize or minimize based on the desired outcome, typically profit maximization or cost minimization.