Let x be the number of units to be sold in the first country and y the number of units to be sold in the second country. Due to the laws of demand, the monopolist must set the price at 97 − (x/10) dollars in the first country and 83 − (y/20) dollars in the second country to sell all units. The cost of producing these units is 20, 000 + 3(x + y). Find the values of x and y that maximize the profit. I got (x,y) = (500, 860) but I'm not completely sure if it's right.

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Let x be the number of units to be sold in the first country and y the number of units to be sold in the second country. Due to the laws of demand, the monopolist must set the price at 97 − (x/10) dollars in the first country and 83 − (y/20) dollars in the second country to sell all units. The cost of producing these units is 20, 000 + 3(x + y). Find the values of x and y that maximize the profit. I got (x,y) = (500, 860) but I'm not completely sure if it's right.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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you are close, but not quite right (x,y) = (470,800) Profit = Revenue - Cost, where Revenue = price*quantity --> P(x,y) = -x^2/10 +94x -y^2/20 +80y -20,000 To maximize this function, take partial derivatives and set them equal to 0 dP/dx = 94 - x/5 = 0 --> x = 470 dP/dy = 80 - y/10 = 0 --> y = 800
Oh i see where i went wrong.. I didn't multiply the (-1) into the cost equation. thank you so much for helping!
no problem :)

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