Question: A consumer has $280 to spend on two commodities, the first of which costs $2 per unit and the second $5 per unit. Suppose that

A consumer has $280 to spend on two commodities, the first of which costs $2 per unit and the second $5 per unit. Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second is given by U(x, y) = 100x^0.25y^0.75.

a. How many units of each commodity should the consumer buy to maximize utility?

b. Compute the Lagrange multiplier λ and interpret in economic terms. (In the context of maximizing utility, λ is called the marginal utility of money.)

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