plant grass 2 days dig up play area o 2 days erect play structure 2 days test equipment safety 1 day DONE START dig up path pour mulch 3 days 1 days 9 paint equipment 2 days dig up basketball court > 4 days pour asphalt 2 days erect baskets 2 day Figure 2: Project tasks with dependencies. An arrow from one task to another indicates that the first task has to be completed before the second task can be begun. Treat the following parts as independent problems. For all parts, write a linear program to solve the problem. Clearly define your variables and explain your constraints. Include the model in the body of the report. Your answer should include both the optimal values of the variables and a diagram of the schedule. Put all the tasks on a time-line, and represent each task by a rectangle of the appropriate length which is labeled with the task number and the length. Here's a schematic example of this format (for the sake of illustration only): Task day 1 day 2 day 3 day 4 day 5 1 2 3 4 Problems 1. Assume there are enough workers available so that is no restriction on the number of tasks that can be performed at the same time. What is the minimum number of days needed to complete all the tasks? What is the schedule? plant grass 2 days dig up play area o 2 days erect play structure 2 days test equipment safety 1 day DONE START dig up path pour mulch 3 days 1 days 9 paint equipment 2 days dig up basketball court > 4 days pour asphalt 2 days erect baskets 2 day Figure 2: Project tasks with dependencies. An arrow from one task to another indicates that the first task has to be completed before the second task can be begun. Treat the following parts as independent problems. For all parts, write a linear program to solve the problem. Clearly define your variables and explain your constraints. Include the model in the body of the report. Your answer should include both the optimal values of the variables and a diagram of the schedule. Put all the tasks on a time-line, and represent each task by a rectangle of the appropriate length which is labeled with the task number and the length. Here's a schematic example of this format (for the sake of illustration only): Task day 1 day 2 day 3 day 4 day 5 1 2 3 4 Problems 1. Assume there are enough workers available so that is no restriction on the number of tasks that can be performed at the same time. What is the minimum number of days needed to complete all the tasks? What is the schedule