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)=100x0.25y0.75 How many units of each commodity should the consumer buy to maximize utility? Compute the Lagrange multiplier λ and interpret in economic terms.

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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)=100x0.25y0.75
How many units of each commodity should the consumer buy to maximize utility? Compute the Lagrange multiplier λ and interpret in economic terms.

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