Implementation of constrOptim in maximization of an objective function

Implementing constrOptim

#Appendix 2: Optimization algorithm  
#Specify the function to be maximized. By default constrOptim performs minimization but the problem can be maximized by setting the fnscale to -1
LP_sol=function(X){
  Y_R=5625-2897*(0.966^X[1])-2728   #Rice N response function
  Y_M=3159-1191*(0.976^X[2])-1968   #Maize N response function
  Y_B=1415-715*(0.950^X[3])-700     #Bean N response function
  Y_FM=2100-923*(0.944^X[4])-1177   #Finger millet N response 
  Y_R1=5665-828*(0.871^X[5])-4837   #Rice P response function
  Y_M1=4474-770*(0.898^X[6])-3704   #Maize P response function
  Y_B1=1138-263*(0.848^X[7])-875    #Bean P response function
  Y_FM1=2101-537*(0.798^X[8])-1564  #Finger millet P response 
  Y_PP=2538-487*(0.758^X[9])-487    #Pigeon Pea P response 
  Y_M2=2502-251*(0.94^X[10])-2251   #Maize K response function
  Y_PP1=2535-127*(0.666^X[11])-2408 #Pigeon Pea K response 
  
  P_R=700;P_M=700;P_B=1000;P_FM=700;P_PP=1500 #Expected commodity prices
  
  P_N=1100; P_P=1200;P_K=1200; #Nutrient cost computed from fertilizer prices per Kg
  
  P=(Y_R*P_R-X[1]*P_N)+(Y_M*P_M-X[2]*P_N)+(Y_B*P_B X[3]*P_N)+(Y_FM*P_FM-X[4]*P_N)+
    (Y_R1*P_R-X[5]*P_P)+(Y_M1*P_M-X[6]*P_P)+(Y_B1*P_B-X[7]*P_P)+(Y_FM1*P_FM-X[8]*P_P)+(Y_PP*P_PP-X[9]*P_P)+
    (Y_M2*P_M-X[10]*P_K)+(Y_PP1*P_PP-X[11]*P_K)   #Net return to fertilizer use function
  return(P)
}
# Assume a budget of TSH 500000,the cost of using 1 kg urea, TSP and KCl to be 1000, 1200, 1200 respectively and expected commodity prices per Kg for Rice, beans, finger millet, pigeon pea and maize to be 700, 1000, 700, 1500 and 700 respectively
#Inequality constraints are stated as:
#1100*X1+1100*X2+1100*X3+1100*X4+1200*X5+1200*X6+1200*X7+1200*X8+1200*X9+1200*X10+1200*X11<=500000
#X1>=0;X2>=0;X3>=0;X4>=0;X5>=0;X6>=0;X7>=0;X8>=0;X9>=0;X10>=0;X11>=0;X12>=0
#All X should be within 0 to 150
#Constraints need to be specified in the form Ax-b>=0
A=matrix(c(-1100,-1100,-1100,-1100,-1200,-1200,-1200,-1200,-1200,-1200,-1200,
           1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,
           0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
           0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,
           0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,
           0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,
           0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,
           0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
           0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,
           0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,
           0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,
           0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1),ncol=11,byrow=T)
B=c(-400000,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150,0,-150)
#Initial guesses of the X values to be maximized
xinit=c(1,1,1,1,1,1,1,1,1,1,1)
# Nelder-Mead method is used to perform the maximization, other options exist e.g. BFGS
xan=constrOptim(theta=xinit, f=LP_sol, grad=NULL, ui=A, ci=B, control=list(fnscale=-1),method = "Nelder-Mead")
#Finally the solution is accessed as below
xan$par
xan$value