3. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg, X1, and (number of) milk cows or calves, X2. Based on fitting the data for milk or meat production the revenue is modelled by a Cobb-Douglas function R(X1, X2) = pX{X} constrained by relation h(X1, X2) = C1X1 + c2X2 = 63. For milk production, the constraint expresses a relation between the average sale price c3 of milk (per day), the average price c of a kg of feed and the price C2 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 cz of meat (per day), the average price c of a kg of feed and the price c2 of a calf (cost per day and based on the annual cost of a calf). The parameters for the two cases have been established by linear regression to be the following: regarding the milk case: p = 445.69, a 0.346, 6 0.542, = 4.00, C2 1.36/d, c3 = 5.38; and, - regarding the meat case: p = 2.348, a = -0.205,b 1.118, C1 4.00, C2 500.0, C3 = 6.02. = (a) Consider the general case first (without substituting any parameter values). De- termine the Lagrangian. Find the FOCs, stationary point and analyse the bordered Hessian to classify the critical point. (Do not eliminate either X or X2). (b) For the general case, verify your findings by repeating the analysis by first elimi- nating X2. Make a comparison of the two analyses. (c) Subsequently use these outcomes to analyse the cases for milk and meat production and draw conclusions. In particular, what improvements in the production and/or mathematical analysis could or should be made, if any? (d) Make a sketch/graph of the solution (either made by hand or by using the computer, e.g., by using Python) for both the milk and meat cases