Q3. A firms production function is given as follows: (5 marks)F(K,L)= AKL; A>0, 0<<1 and 0<<1Where A denotes technology, L and K denote the quantity of labour and capital, respectively,which are used as inputs in the firms production process.a. If wages are denoted by w and rent is denoted by r, and the firm wants to produce 100units of output, derive the firms optimum input demand functions of labour and capital?b. If = 0.5, =0.5, wages is Rs.10, rent is Rs.20 and A= 200, calculate the optimum amounts ofL and K.c. If the value of the parameter for technology A now increases to 300, what happens to thefirms demand for L and K?