A firm uses inputs k l and r to manufacture good q it has a, Business Economics

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A firm uses inputs k l and r to manufacture good q it has a

Question: A firm uses inputs K, L and R to manufacture good Q. It has a budget of £828 and its production function (for positive values of Q) is

Q = 20K + 16L + 12R - 0.2K² - 0.1L² - 0.3R²

If PK = £20, PL = £10 and PR = £6, what is the maximum output it can produce? Assume that second-order conditions for a maximum are satisfied for the relevant Lagrangian.

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