Mathematics
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Please help! A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.15x^2+600x−140500, where P is in dollars, and x is the number of units sold. a. How many units must be sold on a monthly basis to maximize the profit? b. Find the maximum profit

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Lolipop2804

a. The maximum profit is when : P` ( x ) = 0 P` ( x ) = ( - 0.15 x²+ 600 x - 140,500 ) ` P` ( x ) = - 0.3 x + 600 - 0.3 x + 600 = 0 0.3 x = 600 x = 600 : 0.3 = 2,000 Answer: 2000 units must be sold on a monthly basis to maximize the profit. b.  P max = - 0.15 · 2000² + 600 · 2000 - 140,500 = = - 600,000 + 1,200,000 - 140,500 = $459,500 Answer: The maximum profit is $459,500.

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