Extra Exam Exercises (+ solutions) FINAL Mathematics for Premaster
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Course
Mathematics for Premaster
Institution
Tilburg University (UVT)
This document contains 30 extra exam exercises of Mathematics for Premaster that you can use to prepare for your exam. You haven't seen them before, so practicing these would be very helpful.
Exam exercises Mathematics for Premaster FINAL
This is a preview of the extra exam exercises that you can use to prepare for your final. I
have successfully passed the premaster in 2019 myself, and since I received a 9 on
mathematics, I tutored a bunch of students in 2020. For a crash course, I created these
30 exercises with extensive elaboration of the answers myself. This might be very
helpful, because you haven’t practiced with these before.
Please note that copyright belongs to the creator of this document.
It is forbidden to freely distribute this file.
If you have bought this document, you can skip the first 6 pages (until ‘END OF
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Part I
1. Consider a producer with cost function 𝐶(𝑦) = 2𝑦 3 − 6𝑦 2 + 12𝑦. Determine the
minimum price at which the firm produces (i.e., does not make a loss in the
optimum).
2. Determine the supply function of the producer from question 1.
3. Solve the following constrained extremum problem:
.
maximize 𝑧(𝑥, 𝑦) = 𝑥𝑦 + 𝑦 2
subject to 𝑥 + 3𝑦 = 32
where 𝑥 ≥ 0 and 𝑦 ≥ 0
28. Consider the system of linear equations with corresponding extended
coefficient matrix.
.
1 2 1 | 8
[ 0 5 −4 | 10 ].
2
0 −5 𝑡 | 𝑡−8
.
Determine all 𝑡 such that the system is inconsistent.
1 6 4
29. Determine, if possible, the inverse 𝐸 −1 of the matrix 𝐸 = [ −1 3 5 ].
2 3 −1
30. Solve the following maximalization problem:
.
maximize 𝑧(𝑥, 𝑦) = 8𝑥 + 𝑦
such that 4𝑥 + 12𝑦 ≤ 80
2𝑥 + 2𝑦 ≤ 20
𝑥≤7
𝑥 ≥ 0 and 𝑦 ≥ 0
,
,
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