Alice is a farmer who lives in a remote ranch in Texas. She has chosen to improve the way she monitors her corn field. She wants to install wireless sensors to monitor her crops, and collect environmental data. She has a good understanding of electronics, and has decided to design her own sensors and communication infrastructure based on off-the-shelf products. Problem 4) (20 points) Suppose Alice purchases wireless sensor nodes with a maximum transmit power of -5dBm and sensitivity of -90dBm. Assume that the propagation loss model is log-distance with a path loss exponent of 3 and path loss at 1m is 25dB. She wants ensure that there is at least one sensor within 50m of every sensor. Her field is 1000m X 1000m in area. 3.1 How many nodes would she need to purchase such that they can form a network and satisfy her sensing requirement? 3.2 If 5% of those nodes fail, can her network become disconnected? 3.3 How can you ensure that the network remains connected if 10% of the nodes fail? Bonus question (10 points) Alices house adjoins a barn with some animals. The barn then adjoins her corn field. The distance between her house and the field is 500m. She installs the wireless sensor nodes from problem 4 on the animals in the barn to monitor them. How can she collect data from her crops if she places the collection point in her house? How can she leverage the sensors on the animals to mule data from the crops?