My problem is I need to solve for the minimum Vx and minimum Vy so that the projectile clears the gray wall and still hits its mark defined by (x1 + x2). This would be the red trajectory line. I am aware of how to solve the blue trajectory line. The blue line exists in this diagram only to show the difference in scenarios (I am not concerned with the blue line). My givens are:

x1

x2

y1

y2

y3 (which is the target) is always 0

PLEASE NOTE: this is not your typical textbook "throw the ball over the house" problem. It differs in that x1 and x2 are not equal AND y2 is not the maximum height of the trajectory.

How do I go about solving this?? Any ideas?