The optimum output will be when the relationship between LRMC and LRAC.

Option 1 -> Incorrect relationship - LRAC cannot cut LRMC from above at minimum LRAC.

Option 2 -> Incorrect relationship - LRAC cannot cut LRMC from below at minimum LRAC.

Option 3 -> Wrong direction - LRMC cutting from above would indicate maximum point, not minimum.

Option 4 -> Correct relationship - LRMC rises from below and intersects LRAC at its minimum point.

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Hence, Option 4: LRMC cut LRAC from below at the minimum point of LRAC -> At optimum output, the Long Run Marginal Cost (LRMC) curve intersects the Long Run Average Cost (LRAC) curve at its minimum point. Before this point, LRMC lies below LRAC (pulling average cost down). At the minimum point, LRMC equals LRAC. After this point, LRMC rises above LRAC (pulling average cost up). This relationship is fundamental in economics: marginal cost always intersects average cost at the average cost's minimum point, cutting it from below. This represents the most efficient scale of production in the long run -> correct