Suppose milk produced by the cows is determined by the quantity of three different kinds of feed, x1, x2 and x3. Let y denote milk, the production of milk is described by y = ƒ (A, X1, X2, X3), where A stands for the state of
technology. The three different kinds of feed can be purchased under different prices, n, 2 and 3. The dairy farmer is faced with a problem of choosing the combinations of the feeds to maximize output with a budget of $c to spend on the feed.
(1) Derive dy and give an interpretation of each of the terms in the production function.
(2) Derive the first-order conditions for the dairy farmer and give an economic interpretation of the first-order conditions.