From a standard 4x8 sheet, what is the maximum number of cabinet end panels sized 11-1/4 inches by 30 inches that can be cut?

• A. 8
• B. 14
• C. 16
• D. 12

Answer: (D)

Fitting as many panels as possible comes down to lining up the panel’s sides with the sheet edges and counting how many fit along each dimension, then multiplying.

With the 30" side along the 96" length, you can fit floor(96/30) = 3 panels in a row, and across the 48" width you can fit floor(48/11.25) = 4 panels. That gives 3 × 4 = 12 panels.

If you rotate the panels, the 30" side goes along the 48" width, giving floor(48/30) = 1 across, and along the 96" length you can fit floor(96/11.25) = 8. So that arrangement yields 8 panels, which is less.

Trying to mix orientations in different regions doesn’t beat the grid arrangement, because the leftover strips aren’t wide enough to squeeze in another full panel in either orientation. A quick area check shows 13 panels would still be possible by area, but the exact dimensions prevent it, so 12 is the true maximum.