How to minimize a 2-variable cost function
A company uses skilled and unskilled labor to do a particular construction project. The cost of doing the project depends on the number of hours of skilled labor and the number of hours of unskilled labor used, the relationship being:
C=4-3X-4Y+2X^2+3Y^2+xy
Where C is the cost (in thousands of dollars), X is the number of hours (in thousands) of skilled labor, and Y is the number of hours (in thousands) of unskilled labor.
*Find the number of hours of skilled labor and the number of hours of unskilled labor that minimized the cost of doing the project.
*If a license has to be purchased costing $2000 to do this project (and the cost of this license is not included in C), will this alter the answer to part a? If so, how will the answer change?