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Consider a firm that chooses the number of workers and machines to hire

Economics

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Consider a firm that chooses the number of workers and machines to hire. You are brought on as a consultant to help them minimise
costs, but have been told that they must produce y units of output. You know that with L workers and K machines, the firm can produce
(1/4)lnL+(1/2)lnK
units of output. Worker pay is w each and machines cost r each.
e) (1 point) Suppose the CEO wants to aggressively expand production,
so that the new target level is 3y. Could you simply triple your previous recommendation? Justify your answer without math.
f) (1 point) Now suppose the CEO has been reasoned with and instead
sets the new production target at y + 1. Roughly by how much will
optimised costs change? Justiify your answer without solving the optimisation problem again