Difficult# Profit Maximizing on One Input: Marginal Product Edition

MICRO-6KDHRP

Charles "Chuck" Woodward makes bonfires by chucking logs of wood into a pile. The only input required to produce the bonfires is the logs of wood chucked into the pile. The marginal product of a log of wood is $7-\frac{10}{W}$, where $W$ is the amount of logs chucked into the pile ($W$, for "wood", as opposed to $L$, for "logs of wood", to minimize confusion about whether labor or a log of wood is used). A log of wood costs \$9 and a bonfire sells for \$3.