Exercícios MMQD

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PROVA 1 MMQD 
Aluna: Ana Luiza Bomfim Mendes 
Matrícula: 150117086 
 
Q.1 
Item a) 
 
 
 
 
 
 
Q.1 
item b) 
 
 
 
 
 
 
 
 
Q.1 
item c 
 
 
 
Solução ótima computacional 
(utilizei Rstudio) 
 
> library(boot, lib.loc = "C:/Program Files/R/R-4.0.3/library") 
> args(boot::simplex) 
function (a, A1 = NULL, b1 = NULL, A2 = NULL, b2 = NULL, A3 = NULL, 
 b3 = NULL, maxi = FALSE, n.iter = n + 2 * m, eps = 1e-10) 
NULL 
> FO = c(20,24) 
> Rest = matrix(c(3,4,6,2), ncol=2, nrow = 2) 
> b = c(60,32) 
> MAX = simplex(a = FO, A1 = Rest, 
+ b1 = b, maxi = TRUE) 
> MAX 
 
Linear Programming Results 
 
Call : simplex(a = FO, A1 = Rest, b1 = b, maxi = TRUE) 
 
Maximization Problem with Objective Function Coefficients 
x1 x2 
20 24 
 
 
Optimal solution has the following values 
x1 x2 
 4 8 
The optimal value of the objective function is 272 
 
Q.1 
item d) 
 
 
 
 
Análise de sensibilidade (aumento de 4 horas nas horas disponíveis para 
montagem) 
 
> library(boot) 
> args(boot::simplex) 
function (a, A1 = NULL, b1 = NULL, A2 = NULL, b2 = NULL, A3 = NULL, 
 b3 = NULL, maxi = FALSE, n.iter = n + 2 * m, eps = 1e-10) 
NULL 
> FO = c(20,24) 
> Rest = matrix(c(3,4,6,2), ncol=2, nrow = 2) 
> b = c(64,32) 
> MAX = simplex(a = FO, A1 = Rest, 
+ b1 = b, maxi = TRUE) 
> MAX 
 
Linear Programming Results 
 
Call : simplex(a = FO, A1 = Rest, b1 = b, maxi = TRUE) 
 
Maximization Problem with Objective Function Coefficients 
x1 x2 
20 24 
 
 
Optimal solution has the following values 
 x1 x2 
3.555556 8.888889 
The optimal value of the objective function is 284.444444444444. 
 
 
 
 
Análise de sensibilidade (aumento de 4 horas nas horas disponíveis para 
acabamento) 
 
> library(boot) 
> args(boot::simplex) 
function (a, A1 = NULL, b1 = NULL, A2 = NULL, b2 = NULL, A3 = NULL, 
 b3 = NULL, maxi = FALSE, n.iter = n + 2 * m, eps = 1e-10) 
NULL 
> FO = c(20,24) 
> Rest = matrix(c(3,4,6,2), ncol=2, nrow = 2) 
> b = c(60,36) 
> MAX = simplex(a = FO, A1 = Rest, 
+ b1 = b, maxi = TRUE) 
> MAX 
 
Linear Programming Results 
 
Call : simplex(a = FO, A1 = Rest, b1 = b, maxi = TRUE) 
 
Maximization Problem with Objective Function Coefficients 
x1 x2 
20 24 
 
 
Optimal solution has the following values 
 x1 x2 
5.333333 7.333333 
The optimal value of the objective function is 282.666666666667. 
 
 
Q.2 
item a) 
 
 
 
 
 
Q.2) 
item c. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Q.4 
item c 
solução algébrica 
 
 
 
 
 
 
 
 
 
Q.7 
item a 
solução algébrica 
 
 
item b 
 
 
item c 
 
 
 
item d)