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.

Question

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.

dumbcow · Answer

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

anonymous · Answer

Oh i see where i went wrong.. I didn't multiply the (-1) into the cost equation. thank you so much for helping!

dumbcow · Answer

no problem :)