Final answer:
The optimal solution for x in this LP problem is 1y - 10.
Step-by-step explanation:
To find the optimal solution for x in this LP problem, we need to examine the constraints -x + 1y >= 10 and 2x + 4y <= 40. Since the constraints are binding at the optimal solution, it means they are active and determine the feasible region. Let's start with the first constraint -x + 1y >= 10. Rearranging this inequality, we get x <= 1y - 10. Since the constraint is binding, it means that x can take its maximum value, which is the right-hand side of the inequality. Therefore, the optimal solution for x is 1y - 10.