(闭卷,可用计算器) 1 Chinese sportswear firm makes and sells two types of bathing suits, regular and bikini (dental floss") in their modem manufacturing facility in Shenzhen. The company has seen their sales increase sharply, and they find two of their key dep artments with limited capacity. For the near future, only 120 hours of work per week can be scheduled in the cutting department and 80 hours of work per week in the sewing department. Each regular suit takes 5 minutes to cut and 1 minute to sew. Each bikini takes 3 minutes to cut and 4 minutes to sew. Each regular suit contributes $6 to profit, while each bikini contributes S4 to profit. The companys objective is to maximize profits 1)Formulate a linear programming model in algebraic form. (10 r) 2) Based on the computer output (summary of the optimal solution) for this problem. answer the questions below a. If each Regular swimsuit contributed only $2 to profit(instead of $6), how many Regular suits should you produce?(5 ANSWER: The number of Regular swimsuits to produce would be e swimwear company can expand only one department, which one should it be? (Cutting Department or Sewing Department)(5 Circlethe correct answer: Cutting Department sewing Department C. How much can cap acity be increased(in the Department you selected in answer b before it is no longer profitable to produce one of the swimsuits currently being produced (i.e, before the variables in the current solution change)? (5 ANSWER: Amount of increase in minutes is. d. How much more profit will be made if your answer in part c is accepted? (55) ANSWER: Total (not per unit) additional profit in s is
(闭卷，可用计算器) 1 Chinese sportswear firm makes and sells two types of bathing suits, regular and bikini ("dental floss") in their modern manufacturing facility in Shenzhen. The company has seen their sales increase sharply, and they find two of their key departments with limited capacity. For the near future, only 120 hours of work per week can be scheduled in the cutting department and 80 hours of work per week in the sewing department. Each regular suit takes 5 minutes to cut and 1 minute to sew. Each bikini takes 3 minutes to cut and 4 minutes to sew. Each regular suit contributes $6 to profit, while each bikini contributes $4 to profit. The company's objective is to maximize profits. 1) Formulate a linear programming model in algebraic form.(10 分) 2) Based on the computer output (summary of the optimal solution) for this problem, answer the questions below. a. If each Regular swimsuit contributed only $2 to profit (instead of $6), how many Regular suits should you produce?（5 分） b. If the swimwear company can expand only one department, which one should it be? (Cutting Department or Sewing Department) （5 分） Why ________________________________________________________________ c. How much can capacity be increased (in the Department you selected in answer b.) before it is no longer profitable to produce one of the swimsuits currently being produced (i.e., before the variables in the current solution change)? （5 分） d. How much more profit will be made if your answer in part c. is accepted? （5 分） ANSWER: Amount of increase in minutes is: _________________________________ ANSWER: Total (not per unit) additional profit in $ is: __________________________ ANSWER: The number of Regular swimsuits to produce would be: _______________ Circle the correct answer: Cutting Department Sewing Department
Chinese Swimwear Problem Objective Function= p9035294118 R Decision Variables: 847.0588 988. 2352941 R B Objective Function Coefficients 6 4 Constraint Coefficients Left-Hand Sides( LHS)and Right-Hand Sides(RHS) R Total Minutes Cutting 72 7200 Sewing B34 4800 4800 Target Cell(Max) Cell Name Original value nal Value sDS8 Objective Function= 09035:294118 Adjustable Cells Original Value Final Valu SC$11 Regular 08470588235 SDS11 Bikini 0988.2352941 Constraints Name Cell value Formula $D$18 Cutting: Total Minutes 7200 $D$18<=SF$ $19 Sewing: Total Minutes 4800$D$19<=$Fs19 B Final Reduced Objective Allowable Allowable Cel Name Value Cost Coefficient Increase SC$11 Regular 8470588235 0 60.6666667 SD$11 Bikini 04 Constraints Fin Shadow Constraint Allowable Allowable Price RH Side Incre Decrease SD$18 Cutting: Total Minute: 7200 1.176470588 72 SDS19 Sewing: Total Minute 48000.117647059 4800 4800 3360
Chinese Swimwear Problem Objective Function = 9035.294118 R B Decision Variables: 847.0588 988.2352941 R B Objective Function Coefficients: 6 4 Constraint Coefficients Left-Hand Sides (LHS) and Right-Hand Sides (RHS) R B Total Minutes Capacity Cutting: 5 3 7200 <= 7200 Sewing: 1 4 4800 <= 4800 Target Cell (Max) Cell Name Original Value Final Value $D$8 Objective Function = 0 9035.294118 Adjustable Cells Cell Name Original Value Final Value $C$11 Regular 0 847.0588235 $D$11 Bikini 0 988.2352941 Constraints Cell Name Cell Value Formula Status Slack $D$18 Cutting: Total Minutes 7200 $D$18<=$F$18 Binding 0 $D$19 Sewing: Total Minutes 4800 $D$19<=$F$19 Binding 0 Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$11 Regular 847.0588235 0 6 0.666666667 5 $D$11 Bikini 988.2352941 0 4 20 0.4 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$18 Cutting: Total Minutes 7200 1.176470588 7200 16800 3600 $D$19 Sewing: Total Minutes 4800 0.117647059 4800 4800 3360
2对图示网络,(1)用标号法求最大流;(2)求最小截集。其中s为始点,t 为终点,弧上数字为弧的容量。(本题20分) 3 3某工厂生产产品需外购零件A,根据采购数量,价格有一定的折扣。若采购 数量小与800件,价格为100元;若采购数量大与等于800件,价格为90 元。该企业对零件A的年需求量为5000件,每次的订货费为2450元,每件 零件的年存储费率为50元。求最佳采购批量。(本题20分) 4试述排队系统的组成和特征。(本题15分) 5设局中人Ⅰ的赢得矩阵为如下,请解该矩阵对策问题。(本题15分) 62348 A=73849 60723
2 对图示网络，（1）用标号法求最大流；（2）求最小截集。其中 s 为始点，t 为终点，弧上数字为弧的容量。（本题 20 分） s 5 v2 4 2 4 v1 3 t 3 某工厂生产产品需外购零件 A，根据采购数量，价格有一定的折扣。若采购 数量小与 800 件，价格为 100 元；若采购数量大与等于 800 件，价格为 90 元。该企业对零件 A 的年需求量为 5000 件，每次的订货费为 2450 元，每件 零件的年存储费率为 50 元。求最佳采购批量。（本题 20 分） 4 试述排队系统的组成和特征。（本题 15 分） 5 设局中人 I 的赢得矩阵为如下，请解该矩阵对策问题。（本题 15 分） = 6 0 7 2 3 4 6 5 6 7 7 3 8 4 9 6 2 3 4 8 2 3 4 5 0 A
(闭卷,可用计算器) 1 LINEAR PROGRAMMING PROBLEM is the production manager for the Bilco Corporation, which produces three spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with processing times(in hours) as the following table. Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as the following table. Ed Butler wants to determine the mix of spare parts to produce to maximize total profit. Please to formulate a linear programming model in algebraic form(本题10分) PART Machine 1 0.02 0.03 0.05 Machine 2 0.05 0.02 0.04 Profit 50 s40 2)The next five(5)questions refer to the follow sensitivity report Adjustable Cells Final Reduced objective Allowable Allowable Cell Name Value Coefficient Increase Decrease SB$6 Solution Activity 1 3 SCs6 Solution Activity 2 0 SD$6 Solution Activity 3 0 1E+30 Constraints Final Shadow Constraint Allowable Allowable amme Value price R.H. Side Increase Decrease SES2 A Totals 20 7.78 10 12.5 SES3 B Totals 30 SES4 C Totals 18 1E+30 A. What is the optimal objective function value for this problem? (4s) a. It cannot be determined from the given information. d. $90 b.$7.78 s330 c.$240
(闭卷，可用计算器) 1 LINEAR PROGRAMMING PROBLEM 1) Ed Butler is the production manager for the Bilco Corporation, which produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with processing times (in hours) as the following table. Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as the following table. Ed Butler wants to determine the mix of spare parts to produce to maximize total profit. Please to formulate a linear programming model in algebraic form. (本题 10 分) PART A B C Machine 1 0.02 0.03 0.05 Machine 2 0.05 0.02 0.04 Profit $50 $40 $30 2) The next five (5) questions refer to the follow sensitivity report: Adjustable Cells _______________________________________________________________________ Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$6 Solution Activity 1 3 0 30 23 17 $C$6 Solution Activity 2 6 0 40 50 10 $D$6 Solution Activity 3 0 -7 20 7 1E + 30 _______________________________________________________________________ Constraints _______________________________________________________________________ Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$2 A Totals 20 7.78 20 10 12.5 $E$3 B Totals 30 6 30 50 10 $E$4 C Totals 18 0 40 1E + 30 22 _______________________________________________________________________ A. What is the optimal objective function value for this problem? （4 分） a. It cannot be determined from the given information. d. $90. b. $7.78. e. $330. c. $240
B. What is the range of optimality for Activity 2(written as A2 below)? (4 a.-10≤A2≤50. d.30≤A2≤90 c.-4≤A2≤56 coefficient for Activity 1 in the objective function (4分) a. will increase by $77.80 d. will remain the same b. will increase by $23 e. can only be discovered by resolving the problem C. will increase by $30 D. If the right-hand side of Resource A changes to 10, then the objective function value: (4分) a. will decrease by $12.50 d. will remain the same b. will decrease by $125 e. can only be discovered by resolving the roblem C. will decrease by $77.80 E. If the objective function coefficients of Activity 1 and Activity 2 are both increased by $10,then:(4分) a. the optimal solution remains the same d. the shadow prices are b. the optimal solution may or may not remain the same. e. None of the above C. the optimal solution will change 2某项目的各项活动的紧前紧后关系及工期如下表所示。请: 1)绘制该项目的PERT网络图;(7分) 2)在图上计算事项最早时间、事项最迟时间和事项时差。(7分) 3)确定关键路线及工期。(6分) (本题共20分) 紧后活动 活动时间 3 ABCDE C D 5 E E 3某机场专用飞机降落跑道,飞机降落时占用跑道的时间服从负指数分布,平 均每架2分钟,飞机按普阿松流到达机场上空,平均到达间隔时间为2.4分 钟,先到先降落。请回答下列问题 1)此问题属于哪一类排队模型?(5分) 2)飞机在机场上空等待降落的平均时间:(5分)
B. What is the range of optimality for Activity 2 (written as A2 below)? （4 分） a. -10 A2 50. d. 30 A2 90. b. -44 A2 16. e. 20 A2 80. c. -4 A2 56. C If the coefficient for Activity 1 in the objective function changes to $40, then the objective function value: （4 分） a. will increase by $77.80. d. will remain the same. b. will increase by $23. e. can only be discovered by resolving the problem. c. will increase by $30. D. If the right-hand side of Resource A changes to 10, then the objective function value: （4 分） a. will decrease by $12.50. d. will remain the same. b. will decrease by $125. e. can only be discovered by resolving the problem. c. will decrease by $77.80. E. If the objective function coefficients of Activity 1 and Activity 2 are both increased by $10, then: （4 分） a. the optimal solution remains the same. d. the shadow prices are valid. b. the optimal solution may or may not remain the same. e.None of the above. c. the optimal solution will change. 2 某项目的各项活动的紧前紧后关系及工期如下表所示。请： 1）绘制该项目的 PERT 网络图；（7 分） 2）在图上计算事项最早时间、事项最迟时间和事项时差。（7 分） 3）确定关键路线及工期。（6 分） （本题共 20 分） 活 动 紧后活动 活动时间 A B C D E C C, D E E -- 3 5 6 2 3 3 某机场专用飞机降落跑道，飞机降落时占用跑道的时间服从负指数分布，平 均每架 2 分钟，飞机按普阿松流到达机场上空，平均到达间隔时间为 2.4 分 钟，先到先降落。请回答下列问题： 1） 此问题属于哪一类排队模型？（5 分） 2） 飞机在机场上空等待降落的平均时间；（5 分）
3)平均在机场上空等待降落的飞机有几架;(5分) 4)飞机一到达就能降落的概率。(5分) (本题共20分) 4何为存储策略?并论述存储策略的类型及存储模型中通常考虑的费用项目 (本题15分) 5考虑下面的损失矩阵,假设不知道各种自然状态的概率,使用(1)悲观主义 决策准则;(2)等可能决策准则;(3)最小遗憾值决策准则求最优决策。(本 题15分) 自然状态 方案|E 15 17 Ssss 144 E08 317 2 1420 10
3） 平均在机场上空等待降落的飞机有几架；（5 分） 4） 飞机一到达就能降落的概率。（5 分） （本题共 20 分） 4 何为存储策略？并论述存储策略的类型及存储模型中通常考虑的费用项目。 （本题 15 分） 5 考虑下面的损失矩阵，假设不知道各种自然状态的概率，使用（1）悲观主义 决策准则；（2）等可能决策准则；（3）最小遗憾值决策准则 求最优决策。（本 题 15 分） 自 然 状 态 方 案 E1 E2 E3 E4 E5 S1 S2 S3 S4 15 10 0 -6 17 3 14 8 9 2 1 5 14 20 -3 7 19 10 2 0