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[Steps Shown] Native Gardens (NG) is a gardening service that specializes in caring for California native plants. The company hires gardeners on a daily

Question: Native Gardens (NG) is a gardening service that specializes in caring for California native plants. The company hires gardeners on a daily basis ( L ) and purchases pruning shears for them to use ( K ). The daily wage for gardeners is \[w=\\(100\] , the daily rental rate for pruning shears is \[r=\\(20\] , and the competitive market price for a day of garden maintenance is $200. NG has commissioned an econometric study that estimated its production function showing the relationship between number of gardens serviced daily ( Q) and the amounts of labor and capital as follows:

\[Q=4.01+8\ln L+0.5\ln K\] .

Suppose you determine that the estimated production function is statistically significant. How much labor and capital should you employ to maximize profits? Hint: \[\frac{\partial Q}{\partial L}=\frac{8}{L}\] and \[\frac{\partial Q}{\partial K}=\frac{0.5}{K}\] , and do not worry about second-order conditions. What is the firm’s daily profit? How many gardens does it service daily?

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