Factor prices question

Imagine Bapple is producing smartwatches following production function q(L, K) = L
0.5K0.5
.
In the short run, capital is fixed at K¯ = 16. Bapple faces price p = 50 and can hire as many
workers as it would like at a constant wage w = 10.
2.1 A. Find equilibrium labor (L

) and wages.
2.2 B. What are Bapple’s profits at this equilbirum?
2.3 C. Prove that this profit level is a global maximum.

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