Three resource types (RES 1, RES 2, and RES 3) are to be assigned to a certain task. RES 1 working alone can complete the task in 30 days, RES 2 working alone can complete the task in 45 days, and RES 3 working alone can complete the task in 50 days. Suppose 2 units of RES 1 and 1 unit of RES 2 start working on the task together at time 0. One unit of RES 3 is brought in to join the task sometime after time 0. RES 2 quits the task when there is 30% of the task remaining. If the full task is desired to be completed 20 days from time 0, determine when, if at all, RES 3 should be brought in to join the task. Assume that work rates are constant and units of the same resource type have equal work rates. Show all work completely and clearly.