2020年新冠肺炎疫情爆发，M国“拯救地球”国家紧急债券投资策略分析

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\u2009\u2009\u2009\u2009= 4.45x1 + 39.89x1 + 232.11x1 + 8.0x2 + 58.27x2 + 300.54x2 + 12.55x3 + 180.09x3 + 232.11x3 + 12.55x4 + 39.89x4 + 206.12x4 + 4.45x5 + 18.77x5 + 206.12x5\n\n\u540c\u65f6\uff0c\u6211\u4eec\u9700\u8981\u6ee1\u8db3\u4ee5\u4e0b\u7ea6\u675f\u6761\u4ef6\uff1a\n\u7ea6\u675f\u6761\u4ef61\uff1a\u7531x1 + x2 + x3 + x4 + x5 <= 80\uff08\u603b\u6295\u8d44\u91d1\u989d\u4e0d\u8d85\u8fc78000\u4e07\u7f8e\u5143\uff09\n\u7ea6\u675f\u6761\u4ef62\uff1a\u7531x1 >= 0.2 * (x1 + x2 + x3 + x4 + x5)\uff08\u836f\u8853\u5065\u5eb7\u503a\u5238\u8d2d\u4e70\u91d1\u989d\u4e0d\u5f97\u5c11\u4e8e\u603b\u6295\u8d44\u91d1\u989d\u768420\uff05\uff09\n\u7ea6\u675f\u6761\u4ef63\uff1a\u7531x2 + x3 + x4 + x5 >= 0.1 * (x1 + x2 + x3 + x4 + x5)\uff08\u5176\u4ed6\u884c\u4e1a\u503a\u5238\u8d2d\u4e70\u91d1\u989d\u4e0d\u5f97\u5c11\u4e8e\u603b\u6295\u8d44\u91d1\u989d\u768410\uff05\uff09\n\u7ea6\u675f\u6761\u4ef64\uff1a(4.45x1 + 39.89x1 + 232.11x1 + 8.0x2 + 58.27x2 + 300.54x2 + 12.55x3 + 180.09x3 + 232.11x3 + 12.55x4 + 39.89x4 + 206.12x4 + 4.45x5 + 18.77x5 + 206.12x5) / (x1 + x2 + x3 + x4 + x5) >= 2.5\uff08\u5e73\u5747\u98ce\u9669\u7b49\u7ea7\u4e0d\u5f97\u4f4e\u4e8e2.5\uff09\n\u7ea6\u675f\u6761\u4ef65\uff1a(2x1 + 9x1 + 20x1 + 3x2 + 12x2 + 25x2 + 4x3 + 15x3 + 20x3 + 4x4 + 9x4 + 18x4 + 2x5 + 5x5 + 18x5) / (x1 + x2 + x3 + x4 + x5) <= 10\uff08\u5e73\u5747\u5230\u671f\u5e74\u9650\u4e0d\u8d85\u8fc710\u5e74\uff09\n\n\u7b5b\u75d5\u4e0a\u8ff0\uff0c\u6211\u4eec\u53ef\u4ee5\u5efa\u7acb\u5982\u4e0b\u6570\u5b66\u6a21\u578b\u6c42\u89e3\u8fd9\u4e2a\u95ee\u9898\uff1a\n\nMaximize Z = 4.45x1 + 39.89x1 + 232.11x1 + 8.0x2 + 58.27x2 + 300.54x2 + 12.55x3 + 180.09x3 + 232.11x3 + 12.55x4 + 39.89x4 + 206.12x4 + 4.45x5 + 18.77x5 + 206.12x5\n\nSubject to:\nx1 + x2 + x3 + x4 + x5 <= 80\nx1 >= 0.2 * (x1 + x2 + x3 + x4 + x5)\nx2 + x3 + x4 + x5 >= 0.1 * (x1 + x2 + x3 + x4 + x5)\n(4.45x1 + 39.89x1 + 232.11x1 + 8.0x2 + 58.27x2 + 300.54x2 + 12.55x3 + 180.09x3 + 232.11x3 + 12.55x4 + 39.89x4 + 206.12x4 + 4.45x5 + 18.77x5 + 206.12x5) / (x1 + x2 + x3 + x4 + x5) >= 2.5\n(2x1 + 9x1 + 20x1 + 3x2 + 12x2 + 25x2 + 4x3 + 15x3 + 20x3 + 4x4 + 9x4 + 18x4 + 2x5 + 5x5 + 18x5) / (x1 + x2 + x3 + x4 + x5) <= 10\n\n\u4ee5\u4e0b\u7ed9\u51faPython\u7684\u6c42\u89e3\u4ee3\u7801\uff1a\n\npython\nfrom scipy.optimize import linprog\n\n# \u5b9a\u4e49\u76ee\u6807\u51fd\u6570\u7684\u7cfb\u6570\u5411\u91cf\nc = [-4.45, -39.89, -232.11, -8.0, -58.27, -300.54, -12.55, -180.09, -232.11, -12.55, -39.89, -206.12, -4.45, -18.77, -206.12]\n\n# \u5b9a\u4e49\u4e0d\u7b49\u5f0f\u7ea6\u675f\u77e9\u9635\nA = [[1, 1, 1, 1, 1],\n [-0.8, 0, 0, 0, 0],\n [0, -0.9, -0.9, -0.9, -0.9],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]]\n\n# \u5b9a\u4e49\u4e0d\u7b49\u5f0f\u7ea6\u675f\u7684\u53f3\u8fb9\u503c\u5411\u91cf\nb = [80, 0, 0, -2.5, 10]\n\n# \u5b9a\u4e49\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\nx_bounds = [(0, None), (0, None), (0, None), (0, None), (0, None)]\n\n# \u8c03\u7528\u7ebf\u6027\u8ba1\u5212\u6c42\u89e3\u5668\u8fdb\u884c\u6c42\u89e3\nres = linprog(c, A_ub=A, b_ub=b, bounds=x_bounds)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint("Optimal Allocation:")\nfor i, x in enumerate(res.x):\n print(f"Product {i+1}: {x} million dollars")\n\nprint("Total Return: ", -res.fun, " million dollars")\n\n\n\u8fd0\u884c\u4ee5\u4e0b\u4ee3\u7801\uff0c\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684\u503a\u5238\u6295\u8d44\u91d1\u989d\u5206\u914d\u65b9\u6848\u4ee5\u53ca\u603b\u6536\u76ca\u3002