Question: Problem 1. Write a linear program that solves the following problem: Find the maximum value a monic cubic polynomial f(t) = t3 + at2 +

Problem 1. Write a linear program that solves the following problem: Find the maximum value a monic cubic polynomial f(t) = t3 + at2 + bt + c can take at t = 3 if its values at t : 0,1,2 all he in the interval [1,1]. Bonus: What is this maximum value and the polynomial that achieves it? (Use any method you like to nd this, including computer programs or online solvers.)

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