Master STK120 with Confidence! Stressed about acing your STK120 exams and tests? We've got the ultimate study pack to boost your understanding and exam performance. Our comprehensive collection of past STK120 tutorial papers and detailed memos provides valuable insights into exam format, key c...
Question 1
Consider the feasible region given below:
70
60
50
40
30 C
B
20
10
A D
0
0 10 20 F 30 E 40 50 60 70
The objective function is given by: 𝑐 = 2𝑥 + 3𝑦
Let 𝑐 = 3 ∴ 3𝑦 = 3 − 2𝑥
2𝑥
𝑦 =1−
3
a. Find the coordinates of the points that will give a maximum and minimum
value.
Coordinates: Point C (15;30) Max value (green dotted line)
Point A (10;6.67) Min value (purple dotted line)
b. Use the extreme point method (table below) to find the coordinates of the
points and value of the objectve function. Identify the extreme values.
Point Coordinates Value of objective function Extreme value
A (10;6.67) 40.01 Min
B (10;30) 110
C (15;30) 120 Max
D (40;5) 95
E (40;0) 80
F (30;0) 60
, Question 2
The constraints for a LP-problem are:
𝑥 + 2𝑦 ≤ 8
4𝑥 + 2𝑦 ≤ 8
0.5𝑥 + 𝑦 ≤ 3
𝑥, 𝑦 ≥ 0
The objective function for the LP-problem is:
Maximise 4𝑥 + 8𝑦
a. Draw the inequalities and objective function (dotted line) and shade the
feasible region.
A
B
b. Find the coordinates of the point that will maximise the profit.
Let 𝑝 = 8 ∴ 4𝑥 + 8𝑦 = 𝑝
8𝑦 = 𝑝 − 4𝑥
𝑥
𝑦=1−
2
The profit is maximised on the line segment ̅̅̅̅
𝐴𝐵 ((𝑥, 𝑦) = (0,3) up to
(0.67, 2.67))
Use Cramer to find the point B (intersection):
4 2
| |=3
0.5 1
8 2
| | 2
𝑥= 3 1 = = 0.67
3 3
4 8
| | 8
𝑦= 0.5 3 = = 2.67
3 3
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 EFT, 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 this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller thembisilemagudulela. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R70,00. You're not tied to anything after your purchase.