Warehouse W1 holds 60 units and warehouse W2 holds 40 units…

Step 1. The model. The cost is $Z = 4x + 7y + 6(50 - x) + 3(45 - y) = -2x + 4y + 435$ rupees. The rules are $x + y \le 60$ for W1, $x + y \ge 55$ for W2, $x \le 50$, $y \le 45$, $x \ge 0$ and $y \ge 0$.

Step 2. The corners. The lines $x + y = 55$ and $x + y = 60$ cross $y = 45$ at $x = 10$ and $x = 15$, and cross $x = 50$ at $y = 5$ and $y = 10$. These four points are the corners.

Step 3. The costs. At $(10, 45)$, $Z = -20 + 180 + 435 = 595$. At $(15, 45)$, $Z = -30 + 180 + 435 = 585$. At $(50, 10)$, $Z = -100 + 40 + 435 = 375$. At $(50, 5)$, $Z = -100 + 20 + 435 = 355$. The smallest is $355$.

Step 4. Say it. W1 sends $50$ units to S1 and $5$ units to S2. W2 sends $0$ units to S1 and $45 - 5 = 40$ units to S2.