Question: A firm uses only two inputs, \(x_{1}\) and \(x_{2}\) to produce \(y\), and the firm always uses 4 units of \(x_{I}\) with each unit of \(x_{2}\). Input prices are given as \(\mathrm{w}_{1}\) and \(\mathrm{w}_{2}\). (i) Show a hypothetical equilibrium for least costly optimal combinations of inputs with all related diagram and label properly. (ii) Derive the firm's conditional demands for inputs 1 and 2 and illustrate those in a graph. (iii) Derive the firm's total cost function.

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