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Final Exam Reliability & Optim Methods - CVEN 462 & CVEN 562 Spring 2020 Problem 1. (40”) An oil refinery produces four grades of motor oil in three process plants. The refinery incurs a penalty for not meeting the demand of any particular grade of motor oil. The capacities of the plants, the production costs, the demands of the various grades of motor oil, and the penalties are given in the following table: Production cost (\$/day) to manufacture motor oil of grade: Process plant Capacity of the plant (kgal/day) 1 2 3 4 1 100 750 900 1000 1200 2 150 800 950 1100 1400 3 200 900 1000 1200 1600 Demand (kgal/day) 50 150 100 75 Penalty (per each kilogallon shortage) \$10 \$12 \$16 \$20 (1) Formulate the problem of minimizing the overall cost as a Linear Programming problem. (2) How will you solve this problem using Optimization functions in MATLAB? Please list detailed steps and the final solution Problem 2. (40”) A retail store stocks and sells three different models of TV sets. The store cannot afford to have an inventory worth more than \$45,000 at any time. The TV sets are ordered in lots. It costs \$aj for the store whenever a lot of TV model j is ordered. The cost of one TV set of model j is cj. The demand rate of TV model j is dj units per year. The rate at which the inventory costs accumulate is known to be proportional to the investment in inventory at any time, with qj = 0.5, denoting the constant of proportionality for TV model j. Each TV set occupies an area of sj = 0.40 m2 and the maximum storage space available is 90 m2. The data known from the past experience are given below. TV model j 1 2 3 Ordering cost, aj (\$) 50 80 100 TV model j 1 2 3 Unit cost, cj (\$) 40 120 80 Demand rate, dj 800 400 1200 (1) Formulate the problem of minimizing the average annual cost of ordering and storing the TV sets. (2) How will you solve this problem using Optimization functions in MATLAB? Please list detailed steps and the final solution Problem 3 (10”) Find the solution of the following LP problem graphically: subject to Problem 4 (10”) Problem 5 (20”) This problem is for Graduate Students Only Find the maxima and minima, if any, of the function Problem 6 (30”) This problem is for Graduate Students Only Consider the following three-objective optimization problem: Find X = {x 1 x 2}T to minimize subject to Find the minima of the individual objectives under the stated constraints using fmincon ...
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