= Solution
Allocate the extra orchards evenly, giving three independent orchards to each of the six combinations. Each orchard still has mean <variance> $8$ under the fitted model. Each pruning marginal now uses six orchards and each spray marginal nine, giving
$$
\boxed{\widehat{\operatorname{Var}}(\text{pruning difference})=\frac{16}{6}=\frac83,\qquad
\widehat{\operatorname{Var}}(\text{spray difference})=\frac{16}{9}.}
$$
Both are two-thirds of their original values. The orchard residual <statistical degrees of freedom> increase from $12-6=6$ to $18-6=12$.
\b[Extra orchards improve independent <replication>, give a predicted one-third reduction in contrast <variances>, and improve error estimation.] Both this option and using 45 trees require 540 tree measurements, but extra orchards offer the greater predicted statistical gain under the fitted model. They may cost more to recruit and administer; their suitability and comparability also matter.
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