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Download ISYE 6669 - Deterministic Optimization Exam Test Guide 2026 and more Exams Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity!
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Final Exam Time:2 Hours Instructions: - Answer all questions. Show all work for full credit. ‘tance is allowed. - No collaboration or external a: - Clearly state any assumptions made. Section 1: Linear Programming (LP) (30 points) Question 1 (10 points) Consider the following linear program: maxz = 3x14 5x2 subject to 2x14+3x25 12 x1 +4x2 <8 x1, x2 20 1. Graphically solve the linear program and identify the optimal solution. 2. Verify your solution using the Simplex method. Question 2 (10 points) Consider a company that produces two products, A and B, using two resources, RI and R2. The production data is given below: Product | Profit per Unit | Resource | Usage | Resource 2 Usage A [40 [3 |2 B [50 |2 [5 Resource availability: 18 units of R1 and 15 units of R2. Formulatea linear program to maximize profit. Question 3 (10 points) Use the duality theorem to find the shadow prices of the constraints in the problem from Question L. Section 2: Integer Programming (20 points) Question 4 (10 points) A factory produces two types of machines. The production requires labor and raw materials, given in the table below: Machine Type | Labor Required | Raw Materials Required | Profit per Unit xX |2 hours [3kg | $200 Y | 4 hours |2kg | $300 The factory has a maximum of 40 hours of labor and 30 kg of raw materials. The company must produce at least 3 units of each machine. Formulate this as a Mixed-Integer Linear Program (MILP). Question 5 (10 points) Solve the MILP using the Branch and Bound method for the given constraints. Section 3: Network Optimization (20 points) Question 6 (10 points) Consider a transportation problem with three supply nodes and three demand nodes. The supply and demand data is: Supply Node | Supply Available $1 | 20 82 [30 83 [40 Demand Node | Demand Required D1 [25 D2 [35 D3 [30 Cost per unit transported: |D1|D2|D3 sl]2|4]3 82] 5 |2 [6 833 |7 |4 Formulate and solve the transportation problem using the Northwest Corner Method. Question 7 (10 points) Solve the same problem using the Stepping Stone Method and compare the results. Section 4: Nonlinear Optimization (15 points) Question 8 (15 points) Consider the nonlinear program: max fly) = xA2 + yA2 
