To identify the correct option that matches the given diet problem formulation, let’s break down the problem requirements and the constraints:

1. Objective Function:

We are tasked to minimize the cost function:
$z = 0.6x_1 + 0.35x_2$ where:

• $x_1$ = number of units of grain G1 consumed per day
• $x_2$ = number of units of grain G2 consumed per day.

Thus, the problem involves a minimization objective.

2. Constraints:

From the table of nutrients and their requirements, the constraints are as follows:

1. Starch Requirement:
   $5x_1 + 7x_2 \geq 8$
   (At least 8 units of starch needed).

2. Proteins Requirement:
   $4x_1 + 2x_2 \geq 15$
   (At least 15 units of protein needed).

3. Vitamins Requirement:
   $2x_1 + x_2 \geq 3$
   (At least 3 units of vitamins needed).

4. Non-negativity Constraints:
   $x_1 \geq 0$ and $x_2 \geq 0$.

3. Correct Option:

From the provided options:

• Objective: The objective should be minimize $z = 0.6x_1 + 0.35x_2$, not maximize.
• Constraints: The inequalities should all be $\geq$, not $\leq$, to meet the minimum nutrient requirements.

Verification:

• Option 4 is the only one that correctly matches:
  • Minimization of $z = 0.6x_1 + 0.35x_2$.
  • Constraints:
    $5x_1 + 7x_2 \geq 8$,
    $4x_1 + 2x_2 \geq 15$,
    $2x_1 + x_2 \geq 3$.
  • Non-negativity: $x_1 \geq 0, x_2 \geq 0$.

Final Answer:

Option 4 is correct.

Let me know if you need a detailed explanation on solving this linear programming problem! Below are some related questions for further exploration:

1. What are the graphical methods to solve a linear programming problem?
2. How can the simplex method be applied to solve this problem?
3. What is the feasible region in this particular case?
4. How does the cost function behave at the corner points of the feasible region?
5. What happens if the constraints are changed to “$\leq$” instead of “$\geq$”?

Tip: Always check the objective (minimize or maximize) and the direction of constraints to correctly identify linear programming problems.