Given the following financing project being considered by a venture firm, find the probability of completing the path with the longest expected duration by $17$ weeks; by $24$ weeks. By what date is management $90$ percent sure that this path will be completed?

Time $($weeks$)$

Activity$9$ Optimistic Most Likely Pessimistic

$12$: Collect firm data

$5$

$11$

$11$

$13$: Analyze data

$10$

$10$

$10$

$14$: Determine need

$2$

$5$

$8$

$26$: Determine profitability

$1$

$7$

$13$

$36$: Evaluate risk

$4$

$4$

$10$

$37$: Interview owners

$4$

$7$

$10$

$35$: Check references

$2$

$2$

$2$

$45$: Evaluate industry

$0$

$6$

$6$

$57$: Evaluate economy

$2$

$8$

$14$

$67$: Decide funding

$1$

$4$

$7$

If the venture firm can complete the project for the funder within $18$ weeks, it will receive a bonus of $$10,000.$ But if the project delays beyond $22$ weeks, it must pay a penalty of $$5,000$ due to lost opportunity. If the firm can choose whether or not to bid on this project, what should its decision be if the project is only a breakeven one normally?