Consider the Lego LP: max 2s + 3t subject to: 1s + 3t =0 Suppose you wish to add a constraint that says the total number of pieces (bricks and wheels) that can be used must not exceed 27. (Here, s denotes the number of SUVs and t represents the number of trailers). What is wrong with this constraint? 3s + 4t

Question

Consider the Lego LP: max 2s + 3t subject to: 1s + 3t <= 18 2s + 1t <= 11 s>=0, t>=0 Suppose you wish to add a constraint that says the total number of pieces (bricks and wheels) that can be used must not exceed 27. (Here, s denotes the number of SUVs and t represents the number of trailers). What is wrong with this constraint? 3s + 4t <= 27 (select the best answer)

BlackTom AI · Accepted Answer

To tackle the question, I’ll evaluate what a constraint on the total number of pieces should look like and how the proposed 3s + 4t <= 27 relates to that idea.

Option 1: The right-hand-side is wrong. This suggests that the number 27 on the right-hand side does not correctly reflect the total piece limit. The correctness of the RHS depends on the actual total pieces allowed by the problem context. If the problem states a cap on total pieces and the coefficients 3 and 4 accurately count the pieces per SUV and per trailer, then the RHS could be 27. Without more context, it’s not inherently wrong to have 27 as the cap, so this claim would be incorrect unless you know the intended total pieces are different.

Option 2: Both coefficients are wrong. The coefficients (3 for s and 4 for t) encode the number of pieces per SUV and per trailer, respectively. If SUVs contribute 3 pieces each and trailers contribute 4 pieces each in your model, then these coefficients are correct for a total-piece constraint. Calling both coefficients wrong would require a mismatch between the stated pieces-per-vehicle and the coefficients, which we don’t have evidence for from the prompt alone.

Option 3: The t coefficient is wrong. This asserts that the number of pieces contributed by each trailer is not 4. If, in the underlying Lego model, a trailer consists of 4 pieces, then 4 is correct; if a trailer has a different count, say 5 or 2, then this coefficient would indeed be wrong. Without confirming the actual pieces-per-trailer, we cannot conclude this is definitively incorrect.

Option 4: The s coefficient is wrong. Analogous to Option 3, this claims SUVs contribute a different number of pieces than 3. If an SUV truly has 3 pieces in the model, the coefficient is correct; if not, it’s wrong. Again, the prompt as given does not specify the exact pieces-per-SUV, so this cannot be deemed definitively incorrect.

Option 5: None of the other answers is correct. This option would be chosen if the proposed constraint 3s + 4t <= 27 is actually a valid way to express the total-piece cap given the standard interpretation of how many pieces each vehicle type contributes. If the standard interpretation aligns with 3 pieces per SUV and 4 pieces per trailer and the cap is indeed 27 pieces, then the other statements about the RHS or the coefficients being wrong would be false, making this the correct general response.

Option 6: The inequality (<=) is wrong. The inequality sign (<=) is the usual way to express an upper bound on a resource (pieces, in this case). Using <= keeps the feasible region where the total pieces do not exceed the cap. If the intent is to cap the total, changing to < or = would be inappropriate; the <= form is standard for “not exceed.” Unless there is a specific reason to exclude the bound entirely or to require equality, this option is likely incorrect.

In summary, evaluating the plausibility of each option hinges on the actual count of pieces per SUV and per trailer and the intended total-piece cap. If the conventional interpretation gives 3 pieces per SUV, 4 pieces per trailer, and a cap of 27 pieces, then the constraint 3s + 4t <= 27 is a reasonable representation, and the other statements about wrong coefficients or wrong RHS would not be correct. This reasoning supports selecting the option that asserts none of the other explanations are correct, given the standard modeling assumptions, while recognizing that the exact correctness depends on the precise pieces-per-vehicle counts from the Lego model.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Midterm - Thursday, October 9, 2025 - Requires Respondus LockDown Browser

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