Suppose that a firm makes two products A and B that use the same raw materials. Given a fixed amount of raw materials and a fixed amount of manpower, the firm must decide how much of its resources should be al- located to the production of A and how much to B. The management is aware of the production possibilities curve:

9x2 + 4y2 = 18, 000

...which reflects the limitations on personnel and raw materials available to the firm. A point (x, y) on this curve is called a production schedule for the firm, committing it to produce x units of A and y units of B. The sale of each unit of A yields a $3 profit, whereas each unit of B yields a $4 profit. Assuming that all units produced are sold, find the production schedule that maximizes the profit of the firm.

Would anyone be able to help me out? Thank you in advance.

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