The Miller 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 − 3X1 − 4X2 + 2X21 + 3X22 + X1X2
where C is cost (in thousands of dollars), X1 is the number of hours (in thousands) of skilled labor, and X2 is the number of hours (in thousands) of unskilled labor.
a. Find the number of hours of skilled labor and the number of hours of unskilled labor that will minimize the cost of doing the project.
b. If the Miller Company has to purchase a license costing $2,000 to do this project (and if 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?