question four write the dual mathematical optimization formulation of

Question

Question Four: Write the dual mathematical optimization formulation of the following.
maximize 4x₁ + x₂ + 3x3
subject to
x1 +4x₂
<1
3x₁ x₂ + x3 ≤3
T1, T2, T3 20.
-/nQuestion Three (5 Marks): Solve the following optimization problem using the Simplex Method
Max
s. t.
z = 5x₁ + 4x2
6x1 + 4x2 ≤ 24
1x1 + 2x₂ ≤ 6
-x₁ + x₂ ≤1
0≤x₂≤2
x1 ≥ 0
(1)
(2)
(4)
(5)/nQuestion Two (5 Marks): Solve the following optimization problem using the Graphic Method
Max
s. t.
z = 5x₁ + 4x₂
6x₁ + 4 x₂ < 24
1x₁ + 2x₂ ≤ 6
-x₁+ x2 ≤1
0 ≤ x₂ ≤2
x₁ ≥ 0
(1)
(2)
(3)
(4)
(5)/nAnswer each question and show your answer.
Question One (5 Marks): Formulate the following problem into a mathematical model.
T-shirts (600)
Front ($25/dz.)
Back/front ($35/dz.)
TECH
BOWL
CHAMPS
Sweatshirt F
Sweatshirt - B/F
T-shirt - F
T-shirt - B/F
Sweatshirts (500)
Front ($36/dz.)
BOWL
CHAMPS
1,200 Standard
size boxes
Processing
Time (hr)
Per dozen
0.10
0.25
0.08
0.21
Back/front ($548/dz.)
PORE
Cost
Profit
($)
($)
per dozen per dozen
$36
$90
48
125
25
45
35
65