Clara's utility function is U(X, Y)  (X  2) (Y  1) .If Clara's marginal rate of substitution is 6 and she is consuming 8 units of good X, how many units of good Y is she consuming?

A) 14
B) 60
C) 59
D) 6
E) 13

The marginal rate of substitution (MRS) is defined as the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility. Mathematically, MRS = ΔY/ΔX.
In this case, we are given that Clara's MRS is 6. That is, she is willing to give up 6 units of good X for an additional unit of good Y while maintaining the same level of utility. Therefore, we can set up the following equation:
6 = ΔY/ΔX
Solving for ΔY, we get:
ΔY = 6ΔX
We also know that Clara is consuming 8 units of good X. Therefore, we can find her consumption of good Y as follows:
U(X,Y) =  (X  2)(Y  1)
Taking partial derivatives with respect to X and Y, we can find Clara's marginal utility of X (MUx) and marginal utility of Y (MUy) as follows:
MUx = F1F1F12(Y  1)/(X  2)
MUy = (X  2)/Y
Dividing MUx by MUy, we get Clara's MRS as:
MRS = (MUx/MUy) = (Y/X) * (F1F1F12/())
We can now solve for Y by substituting the values we know:
6 = ΔY/ΔX = (Y-X/F1F1F12)/(X/F1F1F12) = (Y/X) - (/(X  2))
Simplifying, we get:
(Y/X) = ( + 6)/(/2) = 59
Therefore, Clara is consuming 59 units of good Y. Answer choice C is correct.