A competitive firm has a technology function defined as Q = f(K,L) = K 1/2 + KL. Here, Q is the weekly output, K is unit

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A competitive firm has a technology function defined as Q =
f(K,L) = K 1/2 + KL. Here, Q is the weekly output, K is units of
capital and L is the number of units of labor employed per week.
The price of the output in the market is 10TL, wage rate is 50TL
and capital cost is 25TL.
a) Find the profit maximizing K, L, Q, and the optimal
profit for the company.
b) Suppose in the short run L = L~ = 2. Draw the
technology set and the isoprofit lines considering labor as a
single variable.
c) Suppose in the short run L = L~ = 2. Find the profit
maximizing K and Q for the company. How did the profit change?
Why?