110年 - 110 國立臺灣科技大學_碩士班招生試題_工業工程學研究所系統工程組：作業研究#100721

科目：研究所、轉學考(插大)◆作業研究 | 年份：110年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：研究所、轉學考(插大)◆作業研究

選擇題 (0)

申論題 (10)

(1) Solve the problem by the revised simplex method. (10%)

(2) Construct the dual problem for this primal problem. (10%)

(3) Solve the dual problem by using the complementary slackness theorem. (10%)

(1) Verify that (u, v) is dual feasible. (10%)

(2) Assuming that (u, v) is an optimal dual solution, find an optimal solution of the primal transportation problem using this information. (10%)

(a) Formulate the evolution of the status of the machine as a Markov chain by identifying three possible states at the end of each day, and then constructing the (one-step) transition matrix.(10%)

(b) Find the expected first passage time for all states. Use these results to identify the expected number of full days that the machine will remain operational before the next breakdown after a repair is completed. (10%)

(a) On the average, how many painted cars without completely installed engines will be in the facility? (10%)

(b) On the average, how long will a painted car have to wait before installation of its engine begins? (10%)

5. A wilderness hiker must pack three items: food, first-aid kits, and clothes. The backpack has a capacity of 3 ft³. Each unit of food takes 1 ft³. A first-aid kit occupies 1/4 ft³, and each piece of cloth takes about 1/2 ft³. The hiker assigns the priority weights 3, 4, and 5 to food, first aid, and clothes, respectively, which means that clothes are the most valuable of the three items. From experience, the hiker must take at least one unit of each item and no more than two first-aid kits. How many of each item should the hiker take? (10%)