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(NET 3) Let x_1, x_2, x_3, x_4, and x_5 be positive integers satisfying
x_1 +x_2 +x_3 +x_4 +x_5 = 1000,
x_1 -x_2 +x_3 -x_4 +x_5 > 0,
x_1 +x_2 -x_3 +x_4 -x_5 > 0,
-x_1 +x_2 +x_3 -x_4 +x_5 > 0,
x_1 -x_2 +x_3 +x_4 -x_5 > 0,
-x_1 +x_2 -x_3 +x_4 +x_5 > 0
(a) Find the maximum of (x_1 + x_3)^{x_2+x_4}
(b) In how many different ways can we choose x_1, . . . , x_5 to obtain the desired maximum?

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