Which constraint enforces total production equals 10 tons in the three-product LP?

• A. X1 + X2 + X3 ≤ 10
• B. X1 + X2 + X3 = 10
• C. X1 + X2 + X3 = 20
• D. X1 + X2 + X3 ≥ 10

Answer: (B)

To fix the total amount produced across all products, you need an equality constraint that ties together the production quantities. Since the required total is exactly 10 tons, the sum must be exactly 10: X1 + X2 + X3 = 10.

Using an inequality would let the total be either less than or greater than 10, which contradicts the requirement. Specifically, ≤ 10 would permit producing less than 10, while ≥ 10 would force at least 10 (and likely more). An equality to 20 would set the total to 20, not 10.

With this exact-total constraint, the optimization can still decide how to allocate the 10 tons among the three products, within any other constraints and the chosen objective.