Consider the following short run production function, where is the output level and is Labour input. If the price of output...

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A profit is an income minus an expense. In this problem the expense is and the income is Therefore the profit as a function of is

The graph of this function is a parabola branches down, it reaches its maximum at the vertex. The -coordinate of the vertex is and the coordinate is  

The output level is  

(we can also obtain the same result using differentiation, )

So the answers are: profit is maximized if the firm uses 38 hours of labour, the output level is 1,444, and the maximum profit is 72,200 K.sh.