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The profit of a monopolist from producing quantities x,y and selling these in two markets with...

The profit of a monopolist from producing quantities x,y and selling these in two markets with linear demand curves is x*(10-x)+y*(9-y)-(x+y)^2. Here, ^ denotes power, * multiplication, / division, + addition, - subtraction. The monopolist chooses nonnegative quantities to maximise profit. Assume the nonnegativity constraints do not bind.

Find the quantity x that the monopolist sells in the first market. Write the answer as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols.

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Answer: x = 1.83

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