Question 1186205
Here's how to set up and solve this linear programming problem:

**a. Set up:**

**i. Variables:**

*   x = pounds of chemical A
*   y = pounds of chemical B

**ii. Constraints:**

*   Agent X:  x + 7y ≥ 175
*   Agent Y:  3x + y ≥ 150
*   Weight: x + y ≥ 100
*   Non-negativity: x ≥ 0, y ≥ 0

**iii. Objective Function:**

Minimize Cost (C) = 8x + 6y

**b. Find the minimum cost:**

1.  **Graph the constraints:** Treat each inequality as an equation and plot the lines. Shade the appropriate region based on the inequality.  For example, for x + 7y ≥ 175, plot the line x + 7y = 175, and shade the region *above* and to the *right* of the line. Do this for all constraints.

2.  **Identify the feasible region:** The feasible region is the area where all the shaded regions overlap.

3.  **Find the vertices:** The vertices of the feasible region are the points where the constraint lines intersect. Solve systems of equations to find these intersection points.  The relevant vertices are:

    *   Intersection of x + 7y = 175 and 3x + y = 150: Solving these gives x = 43, y = 19
    *   Intersection of 3x + y = 150 and x + y = 100: Solving these gives x = 25, y = 75
    *   Intersection of x + 7y = 175 and x + y = 100: Solving these gives x = 12.5, y = 87.5

4.  **Evaluate the objective function at each vertex:**

    *   C(43, 19) = 8(43) + 6(19) = 344 + 114 = ₱458
    *   C(25, 75) = 8(25) + 6(75) = 200 + 450 = ₱650
    *   C(12.5, 87.5) = 8(12.5) + 6(87.5) = 100 + 525 = ₱625

5.  **Determine the minimum cost:** The minimum cost is the smallest value of the objective function.

The minimum cost is ₱458.

**c. Determine the best combination of ingredients:**

The best combination of ingredients is the (x, y) values that correspond to the minimum cost.

The minimum cost of ₱458 occurs when x = 43 and y = 19.

Therefore, the best combination is **43 pounds of chemical A and 19 pounds of chemical B**.