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