Milk or meat production Y per day is best explained by the inputs: feed needed per dayin kg$,$ X$1,$ and $($number of$)$ milk cows or calves, X$2.$ Based on fitting the data for milk or meatproduction the revenue is modelled by a Cobb$-$Douglas function R$($X$1,$ X$2)=$ pXa$1$ Xb$2$ constrainedby relation h$($X$1,$ X$2)=$ c$1$X$1+$ c$2$X$2=$ c$3.$ For milk production, the constraint expresses a relationbetween the average sale price c$3$ of milk $($per day$),$ the average price c$1$ of a kg of feed and the pricec$2$ of a milk cow $($cost per day and based on the annual cost of a milk cow$).$ For meat production,the constraint expresses a relation between the average sale price c$3$ of meat $($per day$),$ the averageprice c$1$ of a kg of feed and the price c$2$ of a calf $($cost per day and based on the annual cost of acalf$).$ The parameters for the two cases have been established by linear regression of data to bethe following:$$ regarding the milk case: p $=445\mathrm{.}69,$ a $=0\mathrm{.}346,$ b $=0\mathrm{.}542,$ c$1=4\mathrm{.}00,$ c$2=1\mathrm{.}36/$d$,$ c$3=5\mathrm{.}38$;and,$$ regarding the meat case: p $=2\mathrm{.}348,$ a $=0\mathrm{.}205,$ b $=1\mathrm{.}118,$ c$1=4\mathrm{.}00,$ c$2=500\mathrm{.}0,$ c$3=6\mathrm{.}02.($i$)$ Consider the general case first $($without substituting any parameter values$).$ Determine theLagrangian. Find the FOCs, stationary point and analyse the bordered Hessian to classifythe critical point.