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

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