A key raw material is rationed so that total production, Mathematics

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A key raw material is rationed so that total production

(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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