Question: In the process of implementing a project, you have sub- contracted JAB Enterprise to supply supplements worth 1480 cartons of two varieties X and Y.

In the process of implementing a project, you have sub- contracted JAB Enterprise to supply supplements worth 1480 cartons of two varieties X and Y. Suppose the joint cost function for the two varieties of supplements is given by C = 250X² + 120Y². The quantity of X and Y are not specified; therefore, the firm may decide to supply any combination. The firm wishes to minimize the cost of producing the supplement but meet your demand.

i. Using Lagrangian multiplier technique find the amounts of X and Y that will minimize cost and compute this cost.

ii. Also examine the cost implications of changing this optimal combination so as to produce equal amounts of both products.

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