In an economy with two agents whose utility functions are $$ U_A(x_1,x_2) = \alpha \cdot x_1 + x_2 \hskip 20pt U_B(y_1,y_2) = y_1 \cdot y_2. $$
The given allocations are bundle (4,0) for A and bundle (1,5) for B.
Consider the following question
Taking into consideration the respective utilities for the bundles, we have $U_A=4\alpha$ and $U_B=5$. For this allocation to be a No Envy allocation, it has to be $4\alpha \geq 5$, which means alpha has to be greater than or equal to $\frac{5}{4}$.
Is this the right approach to solve this problem? If its not, please find the solution and show me the steps.