The problem you've uploaded involves formulating a Linear Programming Problem (LPP) to maximize the profits from producing two products $A$ and $B$, subject to machine time constraints and production capacity.

Here's a step-by-step formulation of the LPP:

Given Information:

• Profit on Product A: ₹60 per unit
• Profit on Product B: ₹50 per unit
• Time required by Product A:
  • 10 minutes on Machine I
  • 8 minutes on Machine II
• Time required by Product B:
  • 20 minutes on Machine I
  • 5 minutes on Machine II
• Machine availability:
  • Machine I: 5 hours/day = 300 minutes/day
  • Machine II: 3 hours/day = 180 minutes/day
• The firm can produce at most 100 units of both products combined.

Decision Variables:

• Let $x_1$ be the number of units of Product $A$ produced per day.
• Let $x_2$ be the number of units of Product $B$ produced per day.

Objective Function:

We want to maximize the total profit $Z$: $Z = 60x_1 + 50x_2$

Constraints:

1. Machine I time constraint: $10x_1 + 20x_2 \leq 300 \quad \text{(Machine I is available for 300 minutes)}$
2. Machine II time constraint: $8x_1 + 5x_2 \leq 180 \quad \text{(Machine II is available for 180 minutes)}$
3. Production capacity constraint: $x_1 + x_2 \leq 100 \quad \text{(Total units of both products cannot exceed 100)}$
4. Non-negativity constraint: $x_1 \geq 0, \quad x_2 \geq 0$

Final LPP Formulation:

Maximize: $Z = 60x_1 + 50x_2$ Subject to: $10x_1 + 20x_2 \leq 300$ $8x_1 + 5x_2 \leq 180$ $x_1 + x_2 \leq 100$ $x_1 \geq 0, \quad x_2 \geq 0$

Would you like details on how to solve this LPP, or any clarifications on the formulation?

Here are some related questions:

1. How do you convert this LPP into a graphical representation?
2. What are the conditions under which the constraints would make the system infeasible?
3. What methods can be used to solve this LPP, besides graphical methods?
4. How does the production limit of 100 units impact the optimization?
5. How can we interpret the shadow price in the context of machine time constraints?

Tip: When solving LPPs, always check the feasibility of constraints to avoid unbounded or infeasible solutions.