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(a) The profit obtained by a firm from producing and selling x and y units of two brands of a commodity is given by
P(x, y) = -0.1x2 - 0.2xy - 0.2y2 + 47x + 48y - 600
Find the production levels that maximize profits.
(b) A key raw material is rationed so that total production must be restricted to 200 units. Find the production levels that now maximize profits.
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