The relationship between MRT and MC

MRT	=	marginal rate of transformation rate at which Y must be sacrificed to get another X the size of the slope of the PPF the opportunity cost of X (in terms of the Y given up)

Example:
Suppose the opportunity cost of another X = 2 units of Y
	=>	slope of PPF = 2
	=>	DY/DX = 2
	=>	MCx must = 2.MCy
	=>	MCx/MCy = 2
	=>	Size of slope of PPF = DY/DX = MRT = MCx/MCy = relative cost of X
For example, if MCx=$20 and MCy=$10, then you have free up $20 of resources to get another X, and you have to stop producing 2Y to get the $20 of resources you need.

Proof:
Consider increasing X by switching labor from Y to X:
    DY = MPLy^.DL
    DX = MPLx^.DL
So:

Note:
    (1) The numerator tells you how much money you need to produce another X (MCx).
    (2) The denominator tells you the rate you raise money by cutting production of Y (MCy per Y).
    (3) So the ratio tells you how much Y you need to cut in order to produce another X.