Problem #1: Part a: Consider the function (z) =% , where z R"and Qis nxn symmetric positive definite matrix. Minimize f(z)subject to the linear constraint Az = b where A isan mx n matrix (assume m 0 and r > 0 are weight parameters that reflect your priority in trading off debt reduction and hardship in making payments. The more anxious you are to reduce your debt, the larger the value of should be relative to r. a) Show that this problem can be formulated as a constrained minimization similar to the problem described in Part (a) above with z =[X,,X,, ..., Xg,Ug,U),....,#s ] . Write the corresponding matrices Q and A, and vector b in terms of the parameters g and 7. b) Using your results in part (a) above, solve the problem (numerically) for the following choice of parameters: e g=1r=10 e g=1r=300 For each case, show a bar chart plot of your monthly payments and monthly account balance. Comment on the results<>