A firm makes three products, in quantities X, Y and Z. It wishes to maximize its profit function: π= 8X + 16Y + 4Z − 0.8X2 − 0.8Y2 − Z2 i) However, in order to satisfy customer orders, it must produce a total of 24 items which are either product X or product Y. Show how many of each of its three products it should produce and find the profit it makes.

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