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Unformatted text preview: the quantity Z 1 u ( t ) 2 dt. Find the function u ( t ) that achieves your goal while minimizing the reduction in broadcast time. 4. Luenberger, Section 3.13, problem 20. 1 5. Luenberger, Section 3.13, problem 23. 6. As an application of the preceding problem, suppose that you have a contract to produce hydrogen gas by electrolysis over a period of 1 year. You do this by using a direct current u ( t ). To meet the delivery requirement, Z 1 u ( t ) dt ≥ c 1 . An additional requirement, to encourage production late in the year, is Z 1 tu ( t ) dt ≥ c 2 . You want to meet both requirements while minimizing Z 1 u ( t ) 2 dt, which is proportional to the electric energy dissipated in your system. Solve this problem, and identify for what sets of values of c 1 and c 2 you might overfulﬁll either the ﬁrst or second requirement. 2...
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 Fall '09
 Math, Mass, World Series, broadcast time, trust fund balance

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