Managerial Economics Question using Derivatives...

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 – 3X˅1 – 4X˅2 +2X 2/1 + 3X 2/2 + X˅1X˅2 where C is cost (in thousands of dollars), X˅1 is the number of hours (in thousands) of skilled labor, and X˅2 is the number of hours (in thousands) of skilled labor.

(a) Find the number of hours of skilled labor and the number of hours of unskilled labor that minimizes the cost of doing the project.

This is what I have so far ... ∂C C = 4 – 3X˅1 – 4X˅2 +2X 2/1 + 3X 2/2 + X˅1X˅2 ∂X˅1 -3 + (2 x2) (X^2-1˅1) + X˅2 = 0 -3 + (4)( X˅1) + X˅2 = 0 -3 + 4 X˅1 + X˅2 = 0 AND

∂C    C = 4 – 3X˅1 – 4X˅2 +2X 2/1 + 3X 2/2 + X˅1X˅2
∂X˅2       -4 + (2)(3) (X^2-1˅2) + X˅1 = 0
    -4 + 6X˅2 + X˅1 = 0

According to my book, X˅1 = 14/23 and X˅2 = 13/23, but I am not sure how to arrive at that answer. I know I needed to take the derivative for both X˅1 and X˅2, but I am not sure where to go from here.

(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?

According to my book, there is no change, but I am not sure why. If you could please help me figure out this problem, I would appreciate it. And, please show all the work so that I can rework the problem for myself. Thank you!