As with the model you learnt in class, the human capital production function is linear, but now employs both private investment by the parent in her child as well as public investment ( ): (1) The child's income (when she becomes an adult) also depends on her human capital linearly so that: (2) Finally, the parent's utility function is given by: (3) The decision problem of the parent is to maximize utility given by (3) subject to the budget constraint you obtained in 2(a) given her knowledge of (1) and (2). Characterize the parent's optimization problem - paying particular attention to what are her choice variables (and what are not) - and derive an expression for the optimal level of parent's investment in child's human capital (i.e., ). Interpret the expression you obtained