Problem 2 (10 marks) An I-beam is shown in the figure to the right. Given the following equations and constraints, develop a mathematical model and find the dimensions of a beam

with a minimal cross sectional area. Cross sectional area: Section modulus: Bending moment: Axial force: Bending stress: Axial stress: Stress constraint: Buckling constraint: X₂ ↓ X4 TH A = x₁x₂ + 2x3x4 - 2x₂x4 S = X₁ (X3X4+*1X2) M = 350 P = 140 Og = Op -142* 1000M S OB + Op- 10P A 180 ≤0 (1+%² 1+171 SO And subject to the following constraints on plate thickness and width: x₁:38,40,41 x₂: 1.9, 2.2, 2.4 x3: 28,30,33 X4: 1.1, 1.3, 1.5 ·X₂ cm² cm³ kNm kN MPa MPa MPa