Question 1181641
Here's how to determine the optimal amount of each type of crude oil to refine:

**1. Define the variables:**

*   Let 'x' be the number of barrels of type A crude oil.
*   Let 'y' be the number of barrels of type B crude oil.

**2. Set up the constraints:**

*   **Total barrels constraint:** x + y ≤ 4000  (The refinery can refine at most 4000 barrels per week)
*   **Impurities constraint:** 2x + 3y ≤ 9000 (The refinery can handle no more than 9000 kg of impurities)
*   **Non-negativity constraints:** x ≥ 0 and y ≥ 0 (We can't refine a negative number of barrels)

**3. Define the objective function (profit):**

Profit (P) = 25x + 30y  (We want to maximize this)

**4. Solve the linear programming problem:**

This can be solved graphically or using linear programming techniques (like the simplex method or software tools). Here's the general approach:

*   **Graphically:**
    1.  Plot the constraints on a graph.
    2.  Identify the feasible region (the area that satisfies all constraints).
    3.  Find the corner points of the feasible region.
    4.  Evaluate the objective function at each corner point.
    5.  The corner point that yields the highest profit is the optimal solution.

*   **Linear Programming:** Specialized software or online calculators can solve this type of problem efficiently.

**Solution:**

The optimal solution is to refine:

*   3000 barrels of type A crude oil
*   1000 barrels of type B crude oil

This will result in a maximum profit of R105,000.