Janice is considering which of two grants to apply for: one from the NSF and one from the NIH. The NSF grant is worth $$200,000$ and the deadline is November $1.$ The NIH grant is worth $$300,000$ and is due December $1.$ It will cost her $$25,000$ to apply for the NSF grant. She estimates a $60\%$ probability she will be successful. It will cost her $$40,000$ to apply for the NIH grant and she estimates only a $40\%$ chance of success. If she does apply for the NSF and does not get the grant, she then has the option $($given the different deadlines$)$ of still applying for the NIH grant. However, given the shortened time schedule, it will still cost her $$40$K to apply and her probability of getting the grant drops to $20\%.$ Not getting a grant simply means $$0.$ Create a decision tree telling Janice which grant she should apply for at the moment. Given this tree, Janice should choose at this moment to apply to $($NSF$/$NIH$).$