b$.$ An increase in fixed cost increases the minimum$-$cost output.

False; average total cost reaches its minimum when it intersects with the marginal cost curve. Since changes in fixed cost do not affect marginal cost, the minimum point of average total cost is unchanged.

True; if fixed costs increase, the spreading effect outweighs the diminishing returns effect for more levels of output. Accordingly, the level of output that minimizes marginal cost will be greater with more fixed costs.

True; if fixed costs increase, the spreading effect strengthens relative to the diminishing returns effect. Accordingly, the level of output that minimizes average total cost clies.

$$ False; average total cost reaches its minimum when it intersects with the marginal cost curve. Since changes in fixed cost do not affect marginal cost, the minimum point of average total cost is unchanged.

False; changes in fixed cost do not affect marginal cost, so the point of minimum marginal cost and the minimum$-$cost output do not change.