1a. Outline the procedures in the use of langragian method for solving non linear programming problem 1b. Given the nonlinear programming problem,minimize F(x)=100(x2-x12 )2+ (1-x1)2subject to x1 2+ x22 <= 2 Determine the optimum values of X1and X2 2. Rewrite the following linear and nonlinear problems in matrix notation a. Minimize f(x)= 3x 1+ 2x 2+ x3 subject to g1 (x)=2x 1+ 3x 2+ x 3>= 10 g2(x) = x 1+ 2x 2+ x 3 >=15 b. Optimize f(x) = 4x 1 2+2x2 2+x3 2 -4x 1 x2 subject to x1 + x 2+ x 3 = 15 2x 1 - x 2+ x 3= 15 x2x3 >=0 3. A two factorial experimental design is approximated by F(x1, x2)= 12x 2+ 4x2 2 -12x1x2+ 2x1 You're to determine the maximum value of the factors or variables starting with the initial guess (x2 , x2) = (-1, -2) 4. In many types of processes such as constant pressure filtration or fixed breed ion exchange, the production rate decreases as a function of time. At some optimal time topt production is terminated at (Popm ) and the equipment is cleaned. For one cycle of production and cleaning the overall production rate R(t) = P(t) / (t+t f ) where P(t) is the overall production rate per cycle (mass/time) = t2 + 1.4t + 10 , tf is the cleaning time (assumed to be Constant) and is equals to 5. Calculate the maximum production time. 5a. what is optimization 5b describe 7 chemical processes/units in which optimization can be applied
1a. Outline the procedures in the use of langragian method for solving non linear programming problem
1b. Given the nonlinear programming problem,minimize F(x)=100(x2-x12 )2+ (1-x1)2subject to x1 2+ x22 <= 2 Determine the optimum values of X1and X2
2. Rewrite the following linear and nonlinear problems in matrix notation
a. Minimize f(x)= 3x 1+ 2x 2+ x3
subject to g1 (x)=2x 1+ 3x 2+ x 3>= 10
g2(x) = x 1+ 2x 2+ x 3 >=15
b. Optimize f(x) = 4x 1 2+2x2 2+x3 2 -4x 1 x2
subject to x1 + x 2+ x 3 = 15
2x 1 - x 2+ x 3= 15
x2x3 >=0
3. A two factorial experimental design is approximated by F(x1, x2)= 12x 2+ 4x2 2 -12x1x2+ 2x1 You're to determine the maximum value of the factors or variables starting with the initial guess (x2 , x2) = (-1, -2)
4. In many types of processes such as constant pressure filtration or fixed breed ion exchange, the production rate decreases as a function of time. At some optimal time topt production is terminated at (Popm ) and the equipment is cleaned. For one cycle of production and cleaning the overall production rate R(t) = P(t) / (t+t f ) where P(t) is the overall production rate per cycle (mass/time) = t2 + 1.4t + 10 , tf is the cleaning time (assumed to be Constant) and is equals to 5. Calculate the maximum production time.
5a. what is optimization
5b describe 7 chemical processes/units in which optimization can be applied
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