Other
Mathematik Klausurübungen Lösung
- Course
- Institution
Sommersemester Mathematik Lösungen Übungen für Klausur Mathematik Klausurübungen Lösung
[Show more]
Seller
Follow
valeriapaez
Content preview
LÖSUNGEN ZU DER PROBEKLAUSUR MATHEMATIK IIAufgabe 1.
Matrix A + B AT · B T C T · B (AT 4B) · C A · B · C
a)
Typ nd (1,1) nd (1,3) (4,3)
Aufgabe 2. Die Lösung ist M1 = 10, M2 = 20 und M3 = 10.
Aufgabe 3.
0 1
✓ ◆ 1 2 3 ✓ ◆
2 3 4 1 0 1
a) MRZ = , MZE = @1 2 1 A , MRE =
5 2 1 0 2 0
1 0 1
✓ ◆
10 10 14
M=
8 16 18
✓ ◆
720
b) r =
940
c) Rohmaterialkosten der Zwischenprodukte = 10 20 · MRZ = 120 70 60 , also ist es
günstiger, die Zwischeprodukte einzukaufen.
Aufgabe 4.
a) 0 x 26.
b) E(x) = 260x 10x2 , k(x) = 440 x + 20, k 0 (x) = 440
x2
0
c) k < 0 für alle x 2 [0, 26], also sind die Durchschnittskosten streng monoton fallend im
ganzen Definitionsbereich mit Minimum in x = 26.
d) G(x) = 10x2 + 240x 440.
Break-Even-Points: 10x2 + 240x 440 = 0 ) x1 = 2, x2 = 22. Die Parabel ist nach
unten geö↵net, also ist der Gewinn negativ für die Outputmengen x 2 [0, 2] [ [22, 26].
e) E 0 (x) = 20x + 260 = 0 , x = 13, E 00 (x) = 20 < 0 für alle x, also liegt in x = 13 ein
globales Maximum vor mit dem Wert E(13) = 1690 GE.
Aufgabe 5.
2
a) p(m) = 3m + 32.
2
b) ✏p (m) = 2
3
m+32
m.
3
✏p (21) = 79 . Die Preis reagiert unelastisch auf eine Änderung bei einer Nachfragemenge
21. Eine 1%-ige Erhöhung der Nachfragemenge führt zu einer 0, 77%-igen Senkung des
Preises.
p
c) m = 2%1% = 2 = ✏p (m)
2m
2= 2
3
m+32
() m = 32.
3
Bei einer Menge von 32 ist das der Fall.
Aufgabe 6.
p 1 4
3
a) xr1 (r1 , r2 ) = r13 4 r2 + ln r2 , xr2 (r1 , r2 ) = 16 r1 r2 4 + r1 r12 .
b) dx(r1 , r2 ) = xr1 (r1 , r2 )dx + xr2 (r1 , r2 )dr2 with dr1 = 1 and dr2 = 2.
dx(3, 16) = 55, 13. Die Produktion fällt um etwa 55,13 ME.
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller valeriapaez. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.71. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
58716 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now