Exam

Question 1

Create a linprog program based on
max 6𝑥 − 𝑦
s. t. 4𝑦 − 𝑥 ≥ 10
2𝑥 + 𝑦 ≤ 10
2𝑦 − 𝑥 ≤ 5
𝑥, 𝑦 ∈ ℝ

Answer 1

f = [-6 1]
A = [1 -4;2 1;-1 2]
b = [-10 10 5]
linprog(f,A,b)

Question 2

Probability shop is empty

Answer 2

is just p0

Question 3

probability queue is empty

Answer 3

all shop employees are used
aka if 4 shop employies: p0+p1+p2+p3
aka p0(1+c1+c2+c3+c4)

Question 4

newtons step

Answer 4

minimise 𝑔(𝑡) = 𝑓(𝑥0 − 𝑡𝑓′(𝑥0))
𝑔′(𝑡) = 𝑓′(𝑥0 − 𝑡𝑓′(𝑥0))(−𝑓′(𝑥0)) = 0
solve for t
𝑡 = (𝑥0 − 𝑘𝜋)/𝑓′(𝑥0)
find the smallest positive optimal step size for k
𝑥1 = 𝑥0 − t𝑓′(𝑥0) = 𝑥0 − [(𝑥0 − 𝜋)/𝑓′(𝑥0)]𝑓′(𝑥0)

Question 5

mean service
times

Answer 5

W-Wq