A dairy farmer wishes to have a model for the cow population of his farm. At the beginning of each year, the cows are divided into three groups. Young heifers (aged 0 to 1 year) make up the first group. The second group consists of cows aged 1 to 2 years, and the third group consists of all cows aged 2 years or older. From past statistical data, the following assumptions are made: Each year, 50% of the third group and 80% of the second group of cows produce a single calf. Half are male and half are female. The males are sold shortly after birth. Each year, 20% of the third group die of natural causes. Some cows from the third group are sold for slaughter each year. Assume that the number of cows sold for slaughter is the input and the population of group 3 is the output of the system. Write the state equations for the system and draw a corresponding simulation diagram. Determine the state-variable matrix parameters (A, B, C, D) for this simulation diagram. Find the operational transfer function for the system. Is the system stable? Would the farmer want a stable system?