Answer Happy

Question 4. A plantation is in the business of commercially growing and harvesting trees for lumber. The plantation is divided into 10 grids as shown below: 1 2 3 4 5 67 8 9 10 = { We are planning for the next four years. Each year, the plantation cuts all the trees in some of the grids (and then replants trees in these grids). Use the following decision variable: ſ 1 if trees in grid i are harvested in year t Dit 0 otherwise 1. A profit of Pit is earned if the grid i is harvested in time period t. Write down a linear objective function that represents maximizing total profit. 2. No more than 6 grids can be harvested in a single year. Write linear inequalities to model this constraint. 3. Because trees need time to grow, each grid should be harvested no more than 2 times in the next four years. Write linear inequalities to model this constraint. 4. Ecological considerations require the implementation of following rule: In any given year, the set of unharvested grids must be connected. For example: harvesting grids 1, 2, 5, 6 in time period 1 is not allowed since the unharvested grids are disconnected into two blocks 3,4 and 7, 8, 9, 10. Write linear inequalities to represent the above constraints. You may introduce artificial variables as necessary.