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Two types of tickets are to be sold for a concert. One type costs $30 per ticket and the other type costs$40 per ticket. The promoter of the concert must sell at least 15,000 tickets, including at least 8000 of the $30 tickets and at least 4000 of the$40 tickets. Moreover, the gross receipts must total at least $500,000 in order for the concert to be held. (a) Find a system of inequalities describing the different numbers of tickets that must be sold, and (b) sketch the graph of the system.
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