1. Minimize f[x]= 0.65-[0.75/[1+x2]] – 0.65 tan-1[1/x] in the interval [0,3] by the Fibonacci method using n=6

2. Using Steepest descent methodMinimize x12 – x1x2 + 3x22. Take starting point [1,2]

3. Write short notes on classification of Optimization Problems and state six engineering applications of Optimization

4. A farmer has 1000 acres of land in which he can grow corn, wheat and soybeans. Each acre of corn costs Rs 100 for preparation requires 7 man-days of work and yields a profit of Rs 30. An acre of wheat costs Rs 120 to prepare, requires 10 man-days of work and yields a profit of Rs 40. An acre of soybeans costs Rs 70 to prepare requires 8 man-days of work and yields a profit of Rs 20. If the farmer has Rs 1,00,000 for preparation and can count-on 8000 man days of work, how many acres should be allocated to each crop to maximize the profit.

5. Find minimum of x2 – 2x, 0= x = 1.5 within an interval of uncertainty 0.25 L0 where L0 is the original interval of uncertainty

6. Find the minimum of f=x(x-1.5) by starting from 0.0 with an initial step size of 0.05.

7. Find the minimum of f=x(x-1.5) in the interval (0.0,1.00) to within 10% of the exact value.

8. Minimize f(x) =0.65-[0.75/(1+x2)]-0.65xtan-1(1/x) in the interval [0,3]by the Fibonacci method using n=6.

9. Minimize f(x) =0.65-[0.75/(1+x2)]-0.65xtan-1(1/x) in the interval [0,3]by the Golden Section Method using n=6.

10. Find the minimum of f=L5-5L3-20L+5 by the cubic interpolation method (L=Lamda)