math econ problems, need the answer(15-19) for the homwork step by step in detail...........

C. Minnie hasjust signed a contract to supply ‘i' gadgets. Her production function is giyen by Q[I{,L} = A K""‘L"2, where K is the amount of capital rented and L is the amount of laboremployed. The wage rate is w and the rental rate of cap'rtal is r.15. Write down the l'u'linnie's optimization problem.15. Write down the ?rst order condition[s}_1?. Solye the system of equation obtained from the ?rst order conditions to ?nd the optimalamounts of cap'rtal and labor.13. Write down the second order cond'rtions and checl-t whether they are satis?ed.19. What is l'u'linnie's cost of producing Y gadgets? Calculate all the partial derivatives ofI'u'linnie's cost function.