Consider the following constrained maximization problem: maximize y = x1 + 5 ln x2 subject to k - x1 - x2 = 0, where k is a constant that can be assigned any specific value. a. Show that if k = 10, this problem can be solved as one involving only equality constraints. d. What is the solution for this problem when k = 20? What do you conclude by comparing this solution to the solution for part (a)?

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Consider the following constrained maximization problem:
maximize y = x1 + 5 ln x2
subject to k - x1 - x2 = 0,
where k is a constant that can be assigned any specific value.

a. Show that if k = 10, this problem can be solved as one involving only equality constraints.


d. What is the solution for this problem when k = 20? What do you conclude by comparing this
solution to the solution for part (a)?


Note: This problem involves what is called a “quasi-linear function.” Such functions provide important
examples of some types of behavior in consumer theory—as we shall see.

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