A Cobb-Douglas type short-run production function is given by \[ q = 2\sqrt{L \overline{K}} \] where \( q, L \) and \( K \) are the output, labour and capital, respectively. \( K \) is fixed at \( \overline{K} \). The unit price of \( L \) is \( w \) and the unit price of \( K \) is \( r \). It is given that \( w = 12 \). Considering the above information, which of the following statements is/are CORRECT?
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