Hi! I have a homework question that i need help understanding, please refer to the example question so that u solve the same way that we are required to.

HOMEWORK: (please solve with workings)

The chapter is about Non Linear Programming

Use the Golden Section Search to find (within an interval of 0.5) the approximate optimal solution to:

EXAMPLE QUESTION & ANSWER (please use the same solving steps to solve the homework question above)

Maximize f = 3x - x? subject to 25x83. Use Golden Section Search to determine (within an interval of 0.5), the optimal solution to Maximize :=-x2-1, -1 Proceed to next iteration! Iteration 2 x3 = B2-B, -2)=0.75 -0.618(1.0815)=0.0816 X = X, +, -a)=-0.3315+0.618(1.0815)=0.3369 Thus, S(x)=-1.0067 and 5(x)=-1.1135 Since (x,)> (x), then [w,,B.]-[-0.3315,0.3369) Hence, B; - a; = 0.3369-(-0.3315)=0.6684 > Proceed to next iteration! Iteration 3 x3 =B-H, -a)= 0.3369 -0.618(0.6684) = -0.0762 Xo =z +r(B; -az)=-0.3315+0.618(0.6684)=0.0816 Thus, f(x)=-1.005867 and f(x)=-1.0067 Since f(xs)> $(x), then [..B.]=[-0.3315,0.0816] Hence, B. -a, -0.0816-(-0.3315)=0.4131