Q$1)$ It is desired to solve the following set of equations using an unconstrained optimization method:

$7x^3-10x-y=1,8y^3-11y+x=1$

a$-$ Formulate the corresponding problem. $[5$P$]$

b$-$ To solve the problem, write a MATLAB program to implement the Davidon$-$Fletcher$-$Powell

method using the Fibonacci method of one$-$dimensional search. You are expected to use a finite$-$

difference scheme to evaluate the gradient of the objective function. $[20$P$]$