SOLUTION: a theater contains 500 seats. For an upcoming talent show, the theater manager plans to sell $4 and $5 tickets. He must sell at least 200 $4 tickets and 100 $5 tickets for the show

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Question 27267: a theater contains 500 seats. For an upcoming talent show, the theater manager plans to sell $4 and $5 tickets. He must sell at least 200 $4 tickets and 100 $5 tickets for the show to be produced. He must bring in at least $2000 to break even. How many tickets at each price should be sold to maximize income.
I am asking this because the other time this is asked, there is no answer on it, just a statement that says It's already been answered.
Answer by bmauger(101) (Show Source):
You can put this solution on YOUR website!
Some detail seems to be missing. Obviously if he wants to maximize income, he should sell as many $5 tickets as he can. Since he "must sell at least 200 $4" then he's left with 500-200=300 seats. He should sell all 300 for $5, because that would make him more money than if he sold them for $4, right? He'll then make
$300 profit. Since there's nothing in the problem that implies he won't be able to sell every ticket he puts up for sale, I have to presume that's the answer or something else is missing from the problem.