3. Suppose that QED Inc's production function is given by F {L, K} = til-Lme, where L denotes the quantity of labor and K denotes the quantitl,Ir of capital. In addition, PL is the price of labor per unit of labor (i.e., the wage rate}, PHB is the cost of health benefits per unit of labor, and PK is the price of capital. a} Using the cost minimization approach and given the output constraint (1 = il-Ll'lZKl'r2 and the input prices, PL, PHB, and PK, [no longer set equal to the above initial values], construct the Lagrangian function. Derive the firm's input demand functions for labor and capital: L = g{Q;P. ,PHB,PK); and, K = hlmePHBPK). Derive the firm's long run total cost function, LRTCl'P ,PHE,PK]. b] Given PL 2 $12, PHB = $4, and PK 2 $64, calculate the long run optimal input bundle, (L*,I(*], for producing [lanaidetermined in part c} aboveand the long run total cost at Chi\