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The Modern Language Association plans a three-day meeting. The program committee requests 15 overhead projectors for the first day, 28 for the second day, and 19 for the third day. Projectors may be rented for a single day for $17, and they may be rented for two consecutive days for$30. How many should be rented for a single day and how many should be rented for two consecutive days to minimize rental costs?

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Firstly we are going to set the substitution. We are going to determine the possible ways to rent the projectors for one day or two days in the span of three days. Since there are 33 ways to rent a projector for one day and 22 ways to rent a projector for two days, we are going to label those days as x1x_1, x2x_2, x3x_3, x4x_4, and x5x_5 where x1x_1, x2x_2, and x3x_3 represent the projectors bought in first, second and third day respectively, and x4x_4 and x5x_5 represent the projectors bought in a first and second, and a second and third day respectively.

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