Upload IndustryOR.json

IndustryOR.json

@@ -10,7 +10,7 @@
 {"en_question": "A convenience supermarket is planning to open several chain stores in a newly built residential area in the northwest suburb of the city. For shopping convenience, the distance from any residential area to one of the chain stores should not exceed $800 \\mathrm{~m}$. Table 5-1 shows the new residential areas and the residential areas within a radius of $800 \\mathrm{~m}$ from each of them. Question: What is the minimum number of chain stores the supermarket needs to build among the mentioned residential areas, and in which residential areas should they be built?\n\n| Area Code | Residential Areas within $800 \\mathrm{~m}$ Radius |\n|-----------|---------------------------------------------------|\n| A         | A, C, E, G, H, I                                  |\n| B         | B, H, I                                           |\n| C         | A, C, G, H, I                                     |\n| D         | D, J                                              |\n| E         | A, E, G                                           |\n| F         | F, J, K                                           |\n| G         | A, C, E, G                                        |\n| H         | A, B, C, H, I                                     |\n| I         | A, B, C, H, I                                     |\n| J         | D, F, J, K, L                                     |\n| K         | F, J, K, L                                        |\n| L         | J, K, L                                           |", "en_answer": "3", "difficulty": "Easy", "id": 10}
 {"en_question": "A company produces two types of small motorcycles, where type A is entirely manufactured by the company, and type B is assembled from imported parts. The production, assembly, and inspection time required for each unit of these two products are shown in Table 3.2.\n\nTable 3.2\n\n| Type | Process | | | Selling Price <br> (Yuan/unit) |\n| :---: | :---: | :---: | :---: | :---: |\n| | Manufacturing | Assembly | Inspection | |\n| Type A (hours/unit) | 20 | 5 | 3 | 650 |\n| Type B (hours/unit) | 0 | 7 | 6 | 725 |\n| Max production capacity per week (hours) | 120 | 80 | 40 | |\n| Production cost per hour (Yuan) | 12 | 8 | 10 | |\n\nIf the company's operational goals and targets are as follows:\n\n$p_{1}$ : The total profit per week should be at least 3000 yuan;\n\n$p_{2}$ : At least 5 units of type A motorcycles should be produced per week;\n\n$p_{3}$ : Minimize the idle time of each process as much as possible. The weight coefficients of the three processes are proportional to their hourly costs, and overtime is not allowed.\n\nTry to establish a model for this problem.", "en_answer": "4136.0", "difficulty": "Medium", "id": 11}
 {"en_question": "Red Star Plastics Factory produces six distinct types of plastic containers. Each container type is characterized by a specific volume, market demand, and unit variable production cost, as detailed in Table 5-11.\n\n**Table 5-11: Container Data**\n| Container Type (Code)             | 1    | 2    | 3    | 4    | 5    | 6     |\n| :------------------------------ | :--- | :--- | :--- | :--- | :--- | :---- |\n| Volume ($\\text{cm}^3$)             | 1500 | 2500 | 4000 | 6000 | 9000 | 12000 |\n| Market Demand (units)           | 500  | 550  | 700  | 900  | 400  | 300   |\n| Unit Variable Production Cost (Yuan/unit) | 5    | 8    | 10   | 12   | 16   | 18    |\n\nThe production of any container type necessitates the use of its dedicated specialized equipment. If the decision is made to **activate** the production equipment for a particular container type (i.e., if the production quantity of that type is greater than zero), a fixed setup cost of 1200 Yuan is incurred for that specific equipment.\n\nShould the production quantity of a certain container type be insufficient to meet its direct demand, the factory has the option to utilize other container types with **larger or equal volume** as substitutes to fulfill this unmet demand. For instance, type 2 containers (volume 2500 $\\text{cm}^3$) can be used to satisfy the demand for type 1 containers (requiring a volume of 1500 $\\text{cm}^3$), but type 1 containers cannot be used for type 2 demand. In this problem, the container type codes are pre-sorted in ascending order of their volumes.\n\n**Question:**\nHow should the factory organize its production? The objective is to develop a production plan that minimizes the total cost—comprising the sum of variable production costs for all containers produced and the fixed costs for all activated equipment—while ensuring that the demand for all container types is fully met.", "en_answer": "43200.00","difficulty": "Hard","id": 12}
-{"en_question": "Tom and Jerry just bought a farm in Sunshine Valley, and they are considering using it to plant corn, wheat, soybeans, and sorghum. The profit per acre for planting corn is $1500, the profit per acre for planting wheat is $1200, the profit per acre for planting soybeans is $1800, and the profit per acre for planting sorghum is $1600. To maximize their profit, how many acres of land should they allocate to each crop? Tom and Jerry’s farm has a total area of 100 acres.\n\nThe land area used for planting corn must be at least twice the land area used for planting wheat.\n\nThe land area used for planting soybeans must be at least half the land area used for planting sorghum.\n\nThe land area used for planting wheat must be three times the land area used for planting sorghum.", "en_answer": "43200.00", "difficulty": "Medium", "id": 13}
+{"en_question": "Tom and Jerry just bought a farm in Sunshine Valley, and they are considering using it to plant corn, wheat, soybeans, and sorghum. The profit per acre for planting corn is $1500, the profit per acre for planting wheat is $1200, the profit per acre for planting soybeans is $1800, and the profit per acre for planting sorghum is $1600. To maximize their profit, how many acres of land should they allocate to each crop? Tom and Jerry’s farm has a total area of 100 acres.\n\nThe land area used for planting corn must be at least twice the land area used for planting wheat.\n\nThe land area used for planting soybeans must be at least half the land area used for planting sorghum.\n\nThe land area used for planting wheat must be three times the land area used for planting sorghum.", "en_answer": "180000.0", "difficulty": "Medium", "id": 13}
 {"en_question": "Mary is planning tonight's dinner. In addition to the vegetables she previously considered, she also wants to choose chicken, salmon, or tofu as a source of protein. Each 100 grams of chicken contains 23 grams of protein, each 100 grams of salmon contains 20 grams of protein, and each 100 grams of tofu contains 8 grams of protein. The price of chicken is $3 per 100 grams, salmon is $5 per 100 grams, and tofu is $1.5 per 100 grams. Considering Mary's budget is $20, how should she choose the ingredients to maximize protein intake? Additionally, the total weight of the food should not exceed 800 grams, and she needs to select at least three vegetables and one source of protein.", "en_answer": "1.5333333333333334", "difficulty": "Hard", "id": 14}
 {"en_question": "A certain factory needs to use a special tool over $n$ planning stages. At stage $j$, $r_j$ specialized tools are needed. At the end of this stage, all tools used within this stage must be sent for repair before they can be reused. There are two repair methods: one is slow repair, which is cheaper (costs $b$ per tool) but takes longer ($p$ stages to return); the other is fast repair, which costs $c$ per tool $(c > b)$ and is faster, requiring only $q$ stages to return $(q < p)$. If the repaired tools cannot meet the needs, new ones must be purchased, with a cost of $a$ per new tool $(a > c)$. This special tool will no longer be used after $n$ stages. Determine an optimal plan for purchasing and repairing the tools to minimize the cost spent on tools during the planning period.\\n\\nn = 10  # number of stages\\nr = [3, 5, 2, 4, 6, 5, 4, 3, 2, 1]  # tool requirements per stage, indexing starts at 1\\na = 10  # cost of buying a new tool\\nb = 1   # cost of slow repair\\nc = 3   # cost of fast repair\\np = 3   # slow repair duration\\nq = 1   # fast repair duration", "en_answer": "36", "difficulty": "Medium", "id": 15}
 {"en_question": "A store plans to formulate the purchasing and sales plan for a certain product for the first quarter of next year. It is known that the warehouse capacity of the store can store up to 500 units of the product, and there are 200 units in stock at the end of this year. The store purchases goods once at the beginning of each month. The purchasing and selling prices of the product in each month are shown in Table 1.3.\n\nTable 1.3\n\n| Month | 1 | 2 | 3 |\n| :---: | :---: | :---: | :---: |\n| Purchasing Price (Yuan) | 8 | 6 | 9 |\n| Selling Price (Yuan) | 9 | 8 | 10 |\n\nNow, determine how many units should be purchased and sold each month to maximize the total profit, and express this problem as a linear programming model.", "en_answer": "4100.0", "difficulty": "Easy", "id": 16}