A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC=10Q_(1)+Q_(1)Q_(2)+10Q_(2) where and denote the quantity of items of goods 1 and 2, respectively that are produced. If P1 and P2 denote the corresponding prices then the demand equations are P_(1)=50-Q_(1)+Q_(2) P_(2)=30+2Q_(1)-Q_(2) Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

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