The company produces 3 different products. If Xab = the production of product b in period a, then to indicate that the company's product 3 production in period 2 is at most 350, we write:

Question

The company produces 3 different products. If Xab = the production of product b in period a, then to indicate that the  company's product 3 production in period 2 is at most 350, we write:

BlackTom AI · Accepted Answer

X_ab denotes production in period a of product b, so the variable for period 2 and product 3 is X_23.  
"At most 350" means the quantity cannot exceed 350, which is expressed with the ≤ (less-than-or-equal) relation. Therefore the correct constraint is X_23 ≤ 350.

1) Relevant concepts:
- Subscript convention X_ab: first index a = period, second index b = product.
- "At most" translates to ≤ in inequality notation.

2) Step-by-step mapping:
- Identify period: period 2 → a = 2.
- Identify product: product 3 → b = 3.
- Form variable: X_ab → X_23.
- Apply "at most 350": X_23 ≤ 350.

3) Intermediate mapping shown explicitly:
- X_23 means period 2, product 3.
- "At most 350" → ≤ 350.
- Combine: X_23 ≤ 350.

4) Why this is correct:
This directly encodes the specified single-variable upper bound: the production of product 3 in period 2 cannot exceed 350 units. It uses the given indexing convention exactly as stated.

5) Why the other choices are incorrect:
- X_32 ≤ 350: this refers to period 3, product 2 (indices swapped), not period 2 product 3.
- X_11 + X_21 + X_31 ≥ 350: this sums product 1 across periods (b = 1) and uses ≥ (at least), which is a different quantity and the wrong inequality direction.
- X_31 + X_32 + X_33 ≤ 350: this sums all products in period 3 (a = 3), not product 3 in period 2.
- None of the above: not applicable because a correct option is listed.

Conclusion: The correct formulation is X_23 ≤ 350, which matches the provided answer.

The company produces 3 different products. If Xab = the production of product b in period a, then to indicate that the company's product 3 production in period 2 is at most 350, we write:Single choice

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