LISTA DE REVISÃO 25/11/15

EXERCICIO 1.

Min = 4*d11 + 2*d12+5*d13+11*d21+7*d22+4*d23;!restrições;D11+d12+d13=800;D21+d22+d23=1000;D11+d21=500;D12+d22=400;D13+d23=900;

Global optimal solution found. Objective value: 6900.000 Infeasibilities: 0.000000 Total solver iterations: 1 Elapsed runtime seconds: 0.49

Model Class: LP

Total variables: 6 Nonlinear variables: 0 Integer variables: 0

Total constraints: 6 Nonlinear constraints: 0

Total nonzeros: 18 Nonlinear nonzeros: 0

Variable Value Reduced Cost D11 500.0000 0.000000

D12 300.0000 0.000000 D13 0.000000 6.000000 D21 0.000000 2.000000 D22 100.0000 0.000000 D23 900.0000 0.000000

Row Slack or Surplus Dual Price 1 6900.000 -1.000000 2 0.000000 0.000000 3 0.000000 -5.000000 4 0.000000 -4.000000 5 0.000000 -2.000000 6 0.000000 1.000000

EXERCICIO 2.

Min= 48*a1+48*a2+50*a3+44*a4+56*b1+60*b2+60*b3+68*b4+96*c1+94*c2+90*c3+85*c4+42*d1+44*d2+54*d3+46*d4;!restrições;@bin(A1);@bin(a2);@bin(a3);@bin(a4);@bin(b1);@bin(b2);@bin(b);@bin(b4);@bin(c1);@bin(c2);@bin(c3);@bin(c4);@bin(d1);@bin(d2);@bin(d3);@bin(d4);

a1+a2+a3+a4=1;b1+b2+b3+b4=1;c1+c2+C3+c4=1;d1+d2+d3+D4=1;

a1+b1+c1+d1=1;a2+b2+c2+d2=1;a3+b3+c3+d3=1;a4+b4+c4+d4=1;

Global optimal solution found. Objective value: 234.0000 Objective bound: 234.0000 Infeasibilities: 0.000000 Extended solver steps: 0 Total solver iterations: 0 Elapsed runtime seconds: 0.48

Model Class: MILP

Total variables: 17 Nonlinear variables: 0 Integer variables: 16

Total constraints: 9 Nonlinear constraints: 0

Total nonzeros: 48 Nonlinear nonzeros: 0

Variable Value Reduced Cost A1 0.000000 48.00000 A2 0.000000 48.00000 A3 0.000000 50.00000 A4 1.000000 44.00000 B1 1.000000 -4.000000 B2 0.000000 0.000000 B3 0.000000 0.000000 B4 0.000000 8.000000 C1 0.000000 96.00000 C2 0.000000 94.00000 C3 1.000000 90.00000 C4 0.000000 85.00000 D1 0.000000 42.00000 D2 1.000000 44.00000 D3 0.000000 54.00000 D4 0.000000 46.00000 B 0.000000 0.000000

Row Slack or Surplus Dual Price 1 234.0000 -1.000000 2 0.000000 0.000000 3 0.000000 -60.00000 4 0.000000 0.000000 5 0.000000 0.000000 6 0.000000 0.000000 7 0.000000 0.000000 8 0.000000 0.000000 9 0.000000 0.000000

EXERCICIO 3.

MIN = D*C + (D/Q)* S + (Q/T) * cM;D= demanda anual;C= custo unitário;Q= quantidade por pedido;Cm= custo unitário de manutenção de estoque;S= custo unitário de pedirT= tempo

MIN =2000*25+ (2000/Q)*60+(Q/2)*12;

Local optimal solution found. Objective value: 51697.06 Infeasibilities: 0.000000 Extended solver steps: 5 Best multistart solution found at step: 1 Total solver iterations: 45 Elapsed runtime seconds: 2.74

Model Class: NLP

Total variables: 1 Nonlinear variables: 1 Integer variables: 0

Total constraints: 1

Nonlinear constraints: 1

Total nonzeros: 1 Nonlinear nonzeros: 1

Variable Value Reduced Cost Q 141.4214 0.000000

Row Slack or Surplus Dual Price 1 51697.06 -1.000000

EXERCICIO 4.

Max= (-0.3*(x^2) ) – (0.5 * (x)*(y))- (0.4* (y^2))+85*x +125y -2500;

!restrições;

X+y<=30000;

Global optimal solution found. Objective value: 7347.826 Infeasibilities: 0.000000 Total solver iterations: 9 Elapsed runtime seconds: 0.48 Model is convex quadratic

Model Class: QP

Total variables: 2 Nonlinear variables: 2 Integer variables: 0

Total constraints: 2 Nonlinear constraints: 1

Total nonzeros: 4 Nonlinear nonzeros: 3

Variable Value Reduced Cost X 23.91305 0.8312832E-06 Y 141.3043 0.1186553E-06

Row Slack or Surplus Dual Price 1 7347.826 1.000000 2 29834.78 0.000000

EXERCICIO 5.

Max=(20*(x^(3/2))*y);

!restrições;

X+y<=60000;

Local optimal solution found. Objective value: 0.3278649E+13 Infeasibilities: 0.000000 Extended solver steps: 5 Best multistart solution found at step: 1 Total solver iterations: 42 Elapsed runtime seconds: 2.62

Model Class: NLP

Total variables: 2 Nonlinear variables: 2 Integer variables: 0

Total constraints: 2 Nonlinear constraints: 1

Total nonzeros: 4 Nonlinear nonzeros: 2

Variable Value Reduced Cost X 36000.00 0.000000 Y 24000.00 0.000000

Row Slack or Surplus Dual Price 1 0.3278649E+13 1.000000 2 0.000000 0.1366104E+09