Correct problem 31
Browse files- IndustryOR.json +1 -1
IndustryOR.json
CHANGED
|
@@ -28,7 +28,7 @@
|
|
| 28 |
{"en_question": "Someone has a fund of 300,000 yuan and has the following investment projects in the next three years:\n(1) Investment can be made at the beginning of each year within three years, with an annual profit of 20% of the investment amount, and the principal and interest can be used for investment in the following year;\n(2) Investment is only allowed at the beginning of the first year, and it can be recovered at the end of the second year, with the total principal and interest amounting to 150% of the investment amount, but the investment limit is no more than 150,000 yuan;\n(3) Investment is allowed at the beginning of the second year within three years, and it can be recovered at the end of the third year, with the total principal and interest amounting to 160% of the investment amount, and the investment limit is 200,000 yuan;\n(4) Investment is allowed at the beginning of the third year within three years, and it can be recovered in one year with a profit of 40%, and the investment limit is 100,000 yuan.\nChapter One: Linear Programming and Simplex Method\nTry to determine an investment plan for this person that maximizes the principal and interest at the end of the third year.", "en_answer": "580000", "difficulty": "Medium", "id": 28}
|
| 29 |
{"en_question": "Jieli Company needs to recruit three types of professionals to work in the two regional branches located in Donghai City and Nanjiang City. The demand for different professionals in these regional branches is shown in Table 4-3. After assessing the situation of the applicants, the company has categorized them into 6 types. Table 4-4 lists the specialties each type of person can handle, the specialty they prefer, and the city they prefer to work in. The company's personnel arrangement considers the following three priorities:\n$p_1$: All three types of professionals needed are fully met;\n$p_2$: 8000 recruited personnel meet their preferred specialty;\n$p_3$: 8000 recruited personnel meet their preferred city.\nTry to establish a mathematical model for goal planning accordingly.\n\nTable 4-3\n| Branch Location | Specialty | Demand |\n|-----------------|-----------|--------|\n| Donghai City | 1 | 1000 |\n| Donghai City | 2 | 2000 |\n| Nanjiang City | 3 | 1500 |\n| Nanjiang City | 1 | 2000 |\n| Nanjiang City | 2 | 1000 |\n| Nanjiang City | 3 | 1000 |\n\nTable 4-4\n\n| Type | Number of People | Suitable Specialty | Preferred Specialty | Preferred City |\n|------|------------------|--------------------|---------------------|----------------|\n| 1 | 1500 | 1,2 | 1 | Donghai |\n| 2 | 1500 | 2,3 | 2 | Donghai |\n| 3 | 1500 | 1,3 | 1 | Nanjiang |\n| 4 | 1500 | 1,3 | 3 | Nanjiang |\n| 5 | 1500 | 2,3 | 3 | Donghai |\n| 6 | 1500 | 3 | 3 | Nanjiang |", "en_answer": "11500.0", "difficulty": "Medium", "id": 29}
|
| 30 |
{"en_question": "Suppose a certain animal needs at least $700 \\mathrm{~g}$ of protein, $30 \\mathrm{~g}$ of minerals, and $100 \\mathrm{mg}$ of vitamins daily. There are 5 types of feed available, and the nutritional content and price per gram of each type of feed are shown in Table 1-5:\nTry to formulate a linear programming model that meets the animal's growth needs while minimizing the cost of selecting the feed.\nTable 1-6\n| Feed | Protein (g) | Minerals (g) | Vitamins (mg) | Price (¥/kg) | Feed | Protein (g) | Minerals (g) | Vitamins (mg) | Price (¥/kg) |\n|------|-------------|--------------|---------------|--------------|------|-------------|--------------|---------------|--------------|\n| 1 | 3 | 1 | 0.5 | 0.2 | 4 | 6 | 2 | 2 | 0.3 |\n| 2 | 2 | 0.5 | 1 | 0.7 | 5 | 18 | 0.5 | 0.8 | 0.8 |\n| 3 | 1 | 0.2 | 0.2 | 0.4 | | | | | |", "en_answer": "32.43589743589744", "difficulty": "Easy", "id": 30}
|
| 31 |
-
{"en_question": "A factory produces three types of products: I, II, and III. Each product must undergo two processing stages, A and B. The factory has two types of equipment to complete stage A (A1, A2) and three types of equipment to complete stage B (B1, B2, B3).\n\nThe production rules are as follows:\n- Product I can be processed on any type of A equipment (A1 or A2) and any type of B equipment (B1, B2, or B3).\n- Product II can be processed on any type of A equipment (A1 or A2), but for stage B, it can only be processed on B1 equipment.\n- Product III can only be processed on A2 equipment for stage A and B2 equipment for stage B.\n\nThe detailed data for processing time per piece, costs, sales price, and machine availability is provided in the table below. The objective is to determine the optimal production plan to maximize the factory's total profit.\n\nData Table\n| Equipment | Product I | Product II | Product III | Effective Machine Hours |
|
| 32 |
{"en_question": "A product consists of three components produced by four workshops, each with a limited number of production hours. Table 1.4 below provides the production rates of the three components. The objective is to determine the number of hours each workshop should allocate to each component to maximize the number of completed products. Formulate this problem as a linear programming problem.\n\nTable 1.4\n\n| Workshop | Production Capacity (hours) | Production Rate (units/hour) | | |\n| :------: | :-------------------------: | :--------------------------: | - | - |\n| | | Component 1 | Component 2 | Component 3 |\n| A | 100 | 10 | 15 | 5 |\n| B | 150 | 15 | 10 | 5 |\n| C | 80 | 20 | 5 | 10 |\n| D | 200 | 10 | 15 | 20 |", "en_answer": "2924.0", "difficulty": "Easy", "id": 32}
|
| 33 |
{"en_question": "A wealthy noble passed away, leaving the following inheritance:\n\n- A painting by Caillebotte: $25000\n- A bust of Diocletian: $5000\n- A Yuan dynasty Chinese vase: $20000\n- A 911 Porsche: $40000\n- Three diamonds: each $12000\n- A Louis XV sofa: $3000\n- Two very precious Jack Russell racing dogs: each $3000 (will stipulates they must not be separated)\n- A sculpture from 200 AD: $10000\n- A sailing boat: $15000\n- A Harley Davidson motorcycle: $10000\n- A piece of furniture once belonging to Cavour: $13000,\n\nwhich must be shared between two sons. How to formulate a mathematical program and solve it using COPTPY to minimize the difference in value between the two parts?", "en_answer": "1000.0", "difficulty": "Medium", "id": 33}
|
| 34 |
{"en_question": "The current problem faced by the company is how to use the fewest number of containers to pack the currently needed goods for transportation, while considering the weight of the goods, specific packaging requirements, and inventory limitations. Professional modeling and analysis are needed for a batch of goods’ transportation strategy to ensure maximum utilization of the limited container space.\n\nThe company currently has a batch to be transported, with each container able to hold a maximum of 60 tons of goods and each container used must load at least 18 tons of goods. The goods to be loaded include five types: A, B, C, D, and E, with quantities of 120, 90, 300, 90, and 120 respectively. The weights are 0.5 tons for A, 1 ton for B, 0.4 tons for C, 0.6 tons for D, and 0.65 tons for E. Additionally, to meet specific usage requirements, every time A goods are loaded, at least 1 unit of C must also be loaded, but loading C alone does not require simultaneously loading A; and considering the demand limitation for D goods, each container must load at least 12 units of D.\n\nEstablish an operations research model so that the company can use the fewest number of containers to pack this batch of goods.", "en_answer": "7.0", "difficulty": "Hard", "id": 34}
|
|
|
|
| 28 |
{"en_question": "Someone has a fund of 300,000 yuan and has the following investment projects in the next three years:\n(1) Investment can be made at the beginning of each year within three years, with an annual profit of 20% of the investment amount, and the principal and interest can be used for investment in the following year;\n(2) Investment is only allowed at the beginning of the first year, and it can be recovered at the end of the second year, with the total principal and interest amounting to 150% of the investment amount, but the investment limit is no more than 150,000 yuan;\n(3) Investment is allowed at the beginning of the second year within three years, and it can be recovered at the end of the third year, with the total principal and interest amounting to 160% of the investment amount, and the investment limit is 200,000 yuan;\n(4) Investment is allowed at the beginning of the third year within three years, and it can be recovered in one year with a profit of 40%, and the investment limit is 100,000 yuan.\nChapter One: Linear Programming and Simplex Method\nTry to determine an investment plan for this person that maximizes the principal and interest at the end of the third year.", "en_answer": "580000", "difficulty": "Medium", "id": 28}
|
| 29 |
{"en_question": "Jieli Company needs to recruit three types of professionals to work in the two regional branches located in Donghai City and Nanjiang City. The demand for different professionals in these regional branches is shown in Table 4-3. After assessing the situation of the applicants, the company has categorized them into 6 types. Table 4-4 lists the specialties each type of person can handle, the specialty they prefer, and the city they prefer to work in. The company's personnel arrangement considers the following three priorities:\n$p_1$: All three types of professionals needed are fully met;\n$p_2$: 8000 recruited personnel meet their preferred specialty;\n$p_3$: 8000 recruited personnel meet their preferred city.\nTry to establish a mathematical model for goal planning accordingly.\n\nTable 4-3\n| Branch Location | Specialty | Demand |\n|-----------------|-----------|--------|\n| Donghai City | 1 | 1000 |\n| Donghai City | 2 | 2000 |\n| Nanjiang City | 3 | 1500 |\n| Nanjiang City | 1 | 2000 |\n| Nanjiang City | 2 | 1000 |\n| Nanjiang City | 3 | 1000 |\n\nTable 4-4\n\n| Type | Number of People | Suitable Specialty | Preferred Specialty | Preferred City |\n|------|------------------|--------------------|---------------------|----------------|\n| 1 | 1500 | 1,2 | 1 | Donghai |\n| 2 | 1500 | 2,3 | 2 | Donghai |\n| 3 | 1500 | 1,3 | 1 | Nanjiang |\n| 4 | 1500 | 1,3 | 3 | Nanjiang |\n| 5 | 1500 | 2,3 | 3 | Donghai |\n| 6 | 1500 | 3 | 3 | Nanjiang |", "en_answer": "11500.0", "difficulty": "Medium", "id": 29}
|
| 30 |
{"en_question": "Suppose a certain animal needs at least $700 \\mathrm{~g}$ of protein, $30 \\mathrm{~g}$ of minerals, and $100 \\mathrm{mg}$ of vitamins daily. There are 5 types of feed available, and the nutritional content and price per gram of each type of feed are shown in Table 1-5:\nTry to formulate a linear programming model that meets the animal's growth needs while minimizing the cost of selecting the feed.\nTable 1-6\n| Feed | Protein (g) | Minerals (g) | Vitamins (mg) | Price (¥/kg) | Feed | Protein (g) | Minerals (g) | Vitamins (mg) | Price (¥/kg) |\n|------|-------------|--------------|---------------|--------------|------|-------------|--------------|---------------|--------------|\n| 1 | 3 | 1 | 0.5 | 0.2 | 4 | 6 | 2 | 2 | 0.3 |\n| 2 | 2 | 0.5 | 1 | 0.7 | 5 | 18 | 0.5 | 0.8 | 0.8 |\n| 3 | 1 | 0.2 | 0.2 | 0.4 | | | | | |", "en_answer": "32.43589743589744", "difficulty": "Easy", "id": 30}
|
| 31 |
+
{"en_question": "A factory produces three types of products: I, II, and III. Each product must undergo two processing stages, A and B. The factory has two types of equipment to complete stage A (A1, A2) and three types of equipment to complete stage B (B1, B2, B3).\n\nThe production rules are as follows:\n- Product I can be processed on any type of A equipment (A1 or A2) and any type of B equipment (B1, B2, or B3).\n- Product II can be processed on any type of A equipment (A1 or A2), but for stage B, it can only be processed on B1 equipment.\n- Product III can only be processed on A2 equipment for stage A and B2 equipment for stage B.\n\nThe detailed data for processing time per piece, costs, sales price, and machine availability is provided in the table below. The objective is to determine the optimal production plan to maximize the factory's total profit.\n\nData Table\n| Equipment | Product I | Product II | Product III | Effective Machine Hours | Processing Cost per Machine Hour (Yuan/hour) |\n| :--- | :--- | :--- | :--- | :--- | :--- |\n| A1 | 5 | 10 | - | 6000 | 0.05 |\n| A2 | 7 | 9 | 12 | 10000 | 0.03 |\n| B1 | 6 | 8 | - | 4000 | 0.06 |\n| B2 | 4 | - | 11 | 7000 | 0.11 |\n| B3 | 7 | - | - | 4000 | 0.05 |\n| Raw Material Cost (Yuan/piece) | 0.25 | 0.35 | 0.5 | - | - | \n| Unit Price (Yuan/piece) | 1.25 | 2 | 2.8 | - | - |","en_answer": "1190.41","difficulty": "Hard","id": 31}
|
| 32 |
{"en_question": "A product consists of three components produced by four workshops, each with a limited number of production hours. Table 1.4 below provides the production rates of the three components. The objective is to determine the number of hours each workshop should allocate to each component to maximize the number of completed products. Formulate this problem as a linear programming problem.\n\nTable 1.4\n\n| Workshop | Production Capacity (hours) | Production Rate (units/hour) | | |\n| :------: | :-------------------------: | :--------------------------: | - | - |\n| | | Component 1 | Component 2 | Component 3 |\n| A | 100 | 10 | 15 | 5 |\n| B | 150 | 15 | 10 | 5 |\n| C | 80 | 20 | 5 | 10 |\n| D | 200 | 10 | 15 | 20 |", "en_answer": "2924.0", "difficulty": "Easy", "id": 32}
|
| 33 |
{"en_question": "A wealthy noble passed away, leaving the following inheritance:\n\n- A painting by Caillebotte: $25000\n- A bust of Diocletian: $5000\n- A Yuan dynasty Chinese vase: $20000\n- A 911 Porsche: $40000\n- Three diamonds: each $12000\n- A Louis XV sofa: $3000\n- Two very precious Jack Russell racing dogs: each $3000 (will stipulates they must not be separated)\n- A sculpture from 200 AD: $10000\n- A sailing boat: $15000\n- A Harley Davidson motorcycle: $10000\n- A piece of furniture once belonging to Cavour: $13000,\n\nwhich must be shared between two sons. How to formulate a mathematical program and solve it using COPTPY to minimize the difference in value between the two parts?", "en_answer": "1000.0", "difficulty": "Medium", "id": 33}
|
| 34 |
{"en_question": "The current problem faced by the company is how to use the fewest number of containers to pack the currently needed goods for transportation, while considering the weight of the goods, specific packaging requirements, and inventory limitations. Professional modeling and analysis are needed for a batch of goods’ transportation strategy to ensure maximum utilization of the limited container space.\n\nThe company currently has a batch to be transported, with each container able to hold a maximum of 60 tons of goods and each container used must load at least 18 tons of goods. The goods to be loaded include five types: A, B, C, D, and E, with quantities of 120, 90, 300, 90, and 120 respectively. The weights are 0.5 tons for A, 1 ton for B, 0.4 tons for C, 0.6 tons for D, and 0.65 tons for E. Additionally, to meet specific usage requirements, every time A goods are loaded, at least 1 unit of C must also be loaded, but loading C alone does not require simultaneously loading A; and considering the demand limitation for D goods, each container must load at least 12 units of D.\n\nEstablish an operations research model so that the company can use the fewest number of containers to pack this batch of goods.", "en_answer": "7.0", "difficulty": "Hard", "id": 34}
|