payments <- matrix(c(2000, 1800, 1500, 1600, 2200, 1600, 1400, 1400, 2500, 2000, 1700, 1600), nrow = 3, ncol = 4,byrow=TRUE)
payments 
eps <- 0.01
chiSquare <- function(riskFactors) {
	cartype <- c(1,riskFactors[1:2]) #c(chi11,chi12,chi13)
	age <- riskFactors[3:6] #c(chi21,chi22,chi23,chi24)
	chiSq <- 0
	for (i in 1:3){
	for (j in 1:4){
	chiSq <- chiSq + (payments[i,j] - cartype[i]*age[j])^2/(cartype[i]*age[j])
	}
	}
	return(chiSq )
}

chiSquare(c(2,2,2,2,2,2))

OptRiskFactors <- optim(c(1,1,1,1,1,1),chiSquare, lower = c(eps ,eps ,eps ,eps ,eps ,eps))$par
OptRiskFactors <- c(1,OptRiskFactors)
OptRiskFactors

tariffs <- matrix(0, nrow = 3, ncol = 4)
for (i in 1:3){
for (j in 1:4){
	tariffs[i,j] <- OptRiskFactors[i]*OptRiskFactors[3+j]
	}
	}
tariffs
payments 

totalPayments<-0
totalTariffs<-0
for (i in 1:3){
for (j in 1:4){
	totalPayments <- totalPayments + payments[i,j]
	totalTariffs <- totalTariffs + tariffs[i,j]
	}
	}
totalPayments
totalTariffs