Answer
Let the origin be the lower left front corner of the pallet.
$$x_{CM}=1.2L$$
$$y_{CM}=2.1L$$
Work Step by Step
Suppose each case has mass M and side length L. Let the origin be the lower left front corner of the pallet. Use equations 7-9a and 7-9b.
In the x-direction: There are 5 cases with center of mass at L/2, 3 cases with center of mass at 3L/2, and 2 cases with center of mass at 5L/2.
$$x_{CM}=\frac{(5M)(L/2)+ (3M)(3L/2)+ (2M)(5L/2)}{10M}=1.2L$$
In the y-direction: There is 1 case with center of mass at L/2, 2 cases with center of mass at 3L/2, and 7 cases with center of mass at 5L/2.
$$y_{CM}=\frac{(1M)(L/2)+ (2M)(3L/2)+ (7M)(5L/2)}{10M}=2.1L$$