400\lambda = 100 \Rightarrow \lambda = \frac{1}{4} \] Substitute back: \[ X = 20 \times \frac{1}{4} = 5,\quad Y = 10 \times \frac{1}{4} = 2.5 \] Optimal bundle: (X, Y) = (5, 2.5) c) Maximum utility: \[ U(5, 2.5) = 5 \times 2.5 = 12.5 \] Part 2: Producer Theory Question 2: A firm's cost fu
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