A company plans to produce liquid bath soap using its two factories in Tangerang and Bekasi, both of which will work with the function TC = 3X2+6Y2-XY

X is the output of the factory in Tangerang and Y is the output of the factory in Bekasi. The company's management will try to determine the lowest cost combination between X and Y, and is required to comply with the constraint that the total product must be 20,000 units.

This is done by solving the X constraint and substituting the value into the objective function with X=15-Y

What is the total cost and its derivative value? Explain!