Problem: Every year, a number of trees in the forest are cut down and sold. In order to keep this forest from drying up and harvest every year, every time a tree is cut down, a sapling should be replanted on the spot to keep the total number of forest trees unchanged. The value of a tree for sale depends on its height. At first, the trees in the forest had different heights. We hope to find a plan to cut down trees on the premise of keeping the harvest, so that the cut trees can get the maximum economic value. 1. The model assumes that we divide the trees in the forest into N levels according to their height, and the height of 1 level trees is [0, h 1], which is a seedling of trees, and its economic value is p 1=0, and the height of K-level trees is [hk- 1, Remember the number of K-type trees in the forest in T years. Suppose the trees in the forest are cut down once a year. In order to maintain a stable harvest every year, only a part of the trees can be cut down, and the remaining trees should be supplemented with seedlings. After a year of growth, the height state should be the same as before the last cut, that is, the same as the initial state. Let them be the first kind of trees when they are cut down; Assuming that trees can only grow at a height level at most during the growth period of one year, that is, the first type of trees may enter or stay in the K type, we ignore the trees that died in the two felling, and think that every seedling can grow to harvest after planting. It is assumed that the proportion of trees growing from the middle to the middle after a one-year growth period is the proportion of trees staying in the middle during a growth period. 2. Let the total number of trees in the forest be s, that is, (15- 1), where s is a predetermined number according to the amount of land and the space required by each tree. From the previous analysis, we first defined the tree height state vector and growth matrix: the tree growth equation without cutting is to describe the situation of cutting and compensation for planting trees, and now we introduce the cutting vector and planting matrix: according to the requirements of the problem, we must keep continuous cutting, so the growth of trees must maintain a balanced relationship: the state at the end of the growth period MINUS the cutting amount and cutting amount, plus the number of replanted seedlings, should be equal to the amount at the beginning of the growth period. That is, (15-2) For any nonnegative vector sum y, the solution satisfying the formula (15- 1) is a feasible solution to maintain the sustainable and stable forest harvest. Because the seedlings have no economic value and are not harvested, Y 65438 is selected. From (15-2) (15-3) in equation (15-3), the first equation is the sum of other n- 1 equations, (15-4) because of the amount of logging. In order to choose the harvest strategy with the greatest benefit, we need to find the maximum value of the function under the conditions of (15- 1) and (15-4). This problem is a linear programming problem in mathematics. By using the theory and method of linear programming, the maximum benefit can be obtained by cutting down trees with a certain height without cutting down the rest trees. Using this conclusion, we can find out what kind of tree is cut down and let the cut tree be K-shaped. Then (15-5) is derived from (15-3) and (15-5), and (15-6) is derived from (15-6). Substituting the formula (15-7) into the formula (15- 1), we get (15-8). Finally, we get: (15-9) When various parameters of trees in the forest are given, we use (18).