The image appears to contain a linear programming problem (LPP) with an objective function and constraints. Here's the breakdown of the problem:

Problem:

Objective Function: $\text{Maximize } Z = 2x_1 + 7x_2 + 5x_3$

Subject to Constraints:

1. $x_1 + x_2 + 2x_3 \leq 3$
2. $4x_1 + x_2 + x_3 \leq 5$
3. $x_1, x_2, x_3 \geq 0$

Explanation:

The goal of this problem is to:

1. Maximize the linear objective function $Z = 2x_1 + 7x_2 + 5x_3$.
2. Ensure that the solution satisfies the given constraints $x_1 + x_2 + 2x_3 \leq 3$ and $4x_1 + x_2 + x_3 \leq 5$.
3. The non-negativity conditions $x_1, x_2, x_3 \geq 0$ must also hold.

Steps to Solve:

This is a standard linear programming problem (LPP), which can be solved using:

1. Graphical Method (only for two variables, not ideal here).
2. Simplex Method (most suitable for three variables).
3. Software Tools such as:
   • Excel Solver
   • Python libraries like scipy or pulp
   • MATLAB

Would you like me to solve this using the Simplex Method or provide a step-by-step explanation? Let me know!

Related Questions:

1. What is the Simplex Method, and how does it work for LPP?
2. How can we solve an LPP using Excel Solver?
3. What are feasible and optimal solutions in LPP?
4. Can duality be applied to this LPP, and how does it help?
5. How is sensitivity analysis applied to linear programming problems?

Tip: Always verify that the constraints are consistent and the feasible region exists before solving an LPP.