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문제

상근이는 각기 다른 병에 담긴 세 화학 물질 A, B, C를 가지고 있다. 두 화학 물질을 같은 양만큼 혼합하면, 화학 제품을 얻을 수 있다.

A와 B를 혼합하면 AB가 되고, B와 C를 혼합하면 BC, C와 A를 혼합하면 CA가 된다. (A 하나와 B 하나를 혼합하면 AB 하나를 얻게 된다) AB, BC, CA의 가격은 모두 다르다. 따라서, 만드는 화학 제품에 따라서 얻는 이익은 달라진다. 항상 정수 단위 만큼 두 화학 물질을 혼합할 수 있다.

예를 들어, A를 5만큼, B를 3만큼, C를 7만큼 가지고 있고, 각 화학 제품의 가격은 다음과 같은 경우를 생각해보자.

화학 제품 단위 가격
AB \$100
BC \$30
CA \$80

A 하나와 B하나를 혼합해 AB 하나를 만들면 \$100을 얻게 된다. 그 다음 B 2개와 C 2개를 혼합하면 \$60을 얻게 되고, C 4개와 A 4개를 혼합해 \$320을 얻게 된다. 총 이익은 \$480이 되고 이 이익이 가능한 이익 중 최대값이다. 한 화학 물질은 모두 사용하지 않을 수도 있다. 이 예제에서는 C를 하나 사용하지 않았다.

다른 예로, A가 3개, B가 3개, C가 3개가 있고, AB, BC, CA의 가격이 모두 \$100인 경우를 생각해보자. A 2개와 B 2개를 혼합해 \$200을 얻고, B 1개와 C 1개를 혼합해 \$100을 얻을 수 있다. 마지막으로 C 1개와 A 1개를 섞으면 \$100을 얻는다. 총 이익은 \$400이 되고, 이 값도 가능한 이익 중 최대값이다.

상근이가 가지고 있는 A, B, C의 양과 AB, BC, CA의 가격이 주어졌을 때, 상근이가 얻을 수 있는 최대 이익을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 두 줄로 이루어져 있다. 첫째 줄에는 상근이가 가지고 있는 A, B, C의 양이 주어진다. 둘째 줄에는 AB, BC, CA의 가격이 주어진다. 입력으로 주어지는 모든 숫자는 정수이며, 1보다 크거나 같고, 1,000보다 작거나 같다.

출력

각 테스트 케이스 마다 최대 이익을 출력한다.

예제 입력 1

2
5 3 7
100 30 80
3 3 3
100 100 100

예제 출력 1

480
400
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(A \ud558\ub098\uc640 B \ud558\ub098\ub97c \ud63c\ud569\ud558\uba74 AB \ud558\ub098\ub97c \uc5bb\uac8c \ub41c\ub2e4) AB, BC, CA\uc758 \uac00\uaca9\uc740 \ubaa8\ub450 \ub2e4\ub974\ub2e4. \ub530\ub77c\uc11c, \ub9cc\ub4dc\ub294 \ud654\ud559 \uc81c\ud488\uc5d0 \ub530\ub77c\uc11c \uc5bb\ub294 \uc774\uc775\uc740 \ub2ec\ub77c\uc9c4\ub2e4. \ud56d\uc0c1 \uc815\uc218 \ub2e8\uc704 \ub9cc\ud07c \ub450 \ud654\ud559 \ubb3c\uc9c8\uc744 \ud63c\ud569\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, A\ub97c 5\ub9cc\ud07c, B\ub97c 3\ub9cc\ud07c, C\ub97c 7\ub9cc\ud07c \uac00\uc9c0\uace0 \uc788\uace0, \uac01 \ud654\ud559 \uc81c\ud488\uc758 \uac00\uaca9\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud574\ubcf4\uc790.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:40%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:20%\">\ud654\ud559 \uc81c\ud488<\/th>\r\n\t\t\t<th style=\"width:20%\">\ub2e8\uc704 \uac00\uaca9<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>AB<\/td>\r\n\t\t\t<td>\\$100<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>BC<\/td>\r\n\t\t\t<td>\\$30<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>CA<\/td>\r\n\t\t\t<td>\\$80<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>A \ud558\ub098\uc640 B\ud558\ub098\ub97c \ud63c\ud569\ud574 AB \ud558\ub098\ub97c \ub9cc\ub4e4\uba74 \\$100\uc744 \uc5bb\uac8c \ub41c\ub2e4. \uadf8 \ub2e4\uc74c B 2\uac1c\uc640 C 2\uac1c\ub97c \ud63c\ud569\ud558\uba74 \\$60\uc744 \uc5bb\uac8c \ub418\uace0, C 4\uac1c\uc640 A 4\uac1c\ub97c \ud63c\ud569\ud574 \\$320\uc744 \uc5bb\uac8c \ub41c\ub2e4. \ucd1d \uc774\uc775\uc740 \\$480\uc774 \ub418\uace0 \uc774 \uc774\uc775\uc774 \uac00\ub2a5\ud55c \uc774\uc775 \uc911 \ucd5c\ub300\uac12\uc774\ub2e4. \ud55c \ud654\ud559 \ubb3c\uc9c8\uc740 \ubaa8\ub450 \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uc744 \uc218\ub3c4 \uc788\ub2e4. \uc774 \uc608\uc81c\uc5d0\uc11c\ub294 C\ub97c \ud558\ub098 \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uc558\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ub978 \uc608\ub85c, A\uac00 3\uac1c, B\uac00 3\uac1c, C\uac00 3\uac1c\uac00 \uc788\uace0, AB, BC, CA\uc758 \uac00\uaca9\uc774 \ubaa8\ub450 \\$100\uc778 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud574\ubcf4\uc790. A 2\uac1c\uc640 B 2\uac1c\ub97c \ud63c\ud569\ud574 \\$200\uc744 \uc5bb\uace0, B 1\uac1c\uc640 C 1\uac1c\ub97c \ud63c\ud569\ud574 \\$100\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4. \ub9c8\uc9c0\ub9c9\uc73c\ub85c C 1\uac1c\uc640 A 1\uac1c\ub97c \uc11e\uc73c\uba74 \\$100\uc744 \uc5bb\ub294\ub2e4. \ucd1d \uc774\uc775\uc740 \\$400\uc774 \ub418\uace0, \uc774 \uac12\ub3c4 \uac00\ub2a5\ud55c \uc774\uc775 \uc911 \ucd5c\ub300\uac12\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\uac00 \uac00\uc9c0\uace0 \uc788\ub294 A, B, C\uc758 \uc591\uacfc AB, BC, CA\uc758 \uac00\uaca9\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc0c1\uadfc\uc774\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc774\uc775\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab\uc9f8 \uc904\uc5d0\ub294 \uc0c1\uadfc\uc774\uac00 \uac00\uc9c0\uace0 \uc788\ub294 A, B, C\uc758 \uc591\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 AB, BC, CA\uc758 \uac00\uaca9\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ubaa8\ub4e0 \uc22b\uc790\ub294 \uc815\uc218\uc774\uba70, 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, 1,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4 \ucd5c\ub300 \uc774\uc775\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8901","problem_lang":"1","title":"Chemical Products","description":"<p>We are given three chemicals A, B, and C contained in separated bottles. If we mix any two chemicals in equal units, we get a valuable chemical product. We call AB the mixture of A and B, BC the mixture of B and C, and CA the mixture of C and A (if we mix one unit of A and one unit of B, we get one unit of AB). Because the prices of AB, BC, and CA can be different, the profit obtained by making the products can vary depending on the way the products are made. Assume we can mix any two chemicals only in integer units.&nbsp;<\/p>\r\n\r\n<p>For example, suppose there are 5 units of A, 3 units of B, and 7 units of C. The price of each product is shown in the next table.&nbsp;<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:40%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:20%\">Chemical Product<\/th>\r\n\t\t\t<th style=\"width:20%\">Price(per one unit)<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>AB<\/td>\r\n\t\t\t<td>\\$100<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>BC<\/td>\r\n\t\t\t<td>\\$30<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>CA<\/td>\r\n\t\t\t<td>\\$80<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>If we mix one unit of A and one unit of B, we get \\$100 by making one unit of AB. Next, mixing 2 units of B and 2 units of C, we get \\$60. Finally, mixing 4 units of C and 4 units of A, we get \\$320. The total profit is \\$480, which is the maximum possible. Note that some portion of one chemical can remain unused: one unit of C is unused in this example.&nbsp;<\/p>\r\n\r\n<p>For another example, suppose there are 3 units of A, 3 units of B, and 3 units of C. Each price of AB, BC, and CA is \\$100. If we mix 2 units of A and 2 units of B, we get \\$200. Next, mixing one unit of B and one unit of C, we get \\$100. Finally, mixing one unit of C and one unit of A, we get \\$100. The total profit is \\$400, which is the maximum possible.&nbsp;<\/p>\r\n\r\n<p>Write a program which calculates the maximum profit when the quantities of A, B, C and the prices of AB, BC, CA are given.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case consists of two lines. The first line of each test case contains three integers. The three integers represent the quantities of chemicals A, B, and C. 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출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Daejeon 2011 B번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: koyh1200