Let's say Andre sells T-shirts and hats equal to T and H, respectively.
The revenue from T-shirts sold is 15T dollars.
The revenue from hats sold is 10H dollars.
Andre wants to sell at least 50 items, so T + H ≥ 50.
Andre wants to make sales of at least $600, so 15T + 10H ≥ 600.
Andre knows that the maximum number of T-shirts he can sell is 40, so T ≤ 40.
Andre wants to sell at least twice as many T-shirts as hats, so T ≥ 2H.
Taking into account Andre's constraints, the minimum number of T-shirts sold must be at least twice the minimum number of hats sold.
Since we want to maximize the revenue from hats, we need to make it as large as possible, so Andre sells the maximum allowable T-shirts, which is 40.
Substituting for T in the inequalities 15T + 10H ≥ 600 and T + H ≥ 50, we get 15(2H) + 10H ≥ 600 and 2H + H ≥ 50.
Simplifying the inequalities gives 40H ≥ 600 and 3H ≥ 50.
After solving the inequalities, we get H ≥ 15 and H ≥ 16.66, respectively. The smallest possible integer value for H is 16.
Substituting the value for H gives T = 2H = 2 * 16 = <<2*16=32>>32.
The maximum revenue is 15T + 10H = 15 * 32 + 10 * 16 = $480 + $160 = $640.
Andre can sell a maximum of 32 T-shirts and a minimum of 16 hats to meet his goals. Answer: \boxed{32, 16}.
Andre is organizing a charity event where he plans to sell two types of items: T-shirts and hats. The selling price for a T-shirt is $15, and the selling price for a hat is $10. Andre wants to sell at least 50 items in total and make a minimum of $600 in sales. If he knows that he can sell at most 40 T-shirts, and he wants to sell at least twice as many T-shirts as hats, how many of each item should he sell to meet his goals?
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