Graphical solution; nonlinear program. consider the following nonlinear program:
min f(x1, x2) = x1
s. t. x^2_1\leq x_2
x^2_1 +x^2_2 \leq 4
(a) solve the problem graphically. (feel free to use computer software to plot the nonlinear functions.) make sure to clearly label the constraints, show objective contours, and shade the feasible region. (using matlab software if possible)
(b) is the optimal solution an extreme point of the feasible region? explain.

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.