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Maximum of the Product of Two Numbers

 

Introduction

Find the maximum value of the product of two positive numbers whose sum is 100.

using System;

public class Program
{
    static int Main()
    {
        // Find the maximum value of the product of 
        // two positive numbers whose sum is 100.
        for(int i = 1; i < 100; i++)
            Console.WriteLine("{0,2} + {1,2} = {2,2}\t{3,2} * {4,2} = {5,4}",
                              i, 100 - i, i + (100 - i),
                              i, 100 - i, i * (100 - i));

        Console.WriteLine();
        return 0;
    }
}

This would produce:

 1 + 99 = 100    1 * 99 =   99
 2 + 98 = 100    2 * 98 =  196
 3 + 97 = 100    3 * 97 =  291
 4 + 96 = 100    4 * 96 =  384
 5 + 95 = 100    5 * 95 =  475
 6 + 94 = 100    6 * 94 =  564
 7 + 93 = 100    7 * 93 =  651
 8 + 92 = 100    8 * 92 =  736
 9 + 91 = 100    9 * 91 =  819
10 + 90 = 100   10 * 90 =  900
11 + 89 = 100   11 * 89 =  979
12 + 88 = 100   12 * 88 = 1056
13 + 87 = 100   13 * 87 = 1131
14 + 86 = 100   14 * 86 = 1204
15 + 85 = 100   15 * 85 = 1275
16 + 84 = 100   16 * 84 = 1344
17 + 83 = 100   17 * 83 = 1411
18 + 82 = 100   18 * 82 = 1476
19 + 81 = 100   19 * 81 = 1539
20 + 80 = 100   20 * 80 = 1600
21 + 79 = 100   21 * 79 = 1659
22 + 78 = 100   22 * 78 = 1716
23 + 77 = 100   23 * 77 = 1771
24 + 76 = 100   24 * 76 = 1824
25 + 75 = 100   25 * 75 = 1875
26 + 74 = 100   26 * 74 = 1924
27 + 73 = 100   27 * 73 = 1971
28 + 72 = 100   28 * 72 = 2016
29 + 71 = 100   29 * 71 = 2059
30 + 70 = 100   30 * 70 = 2100
31 + 69 = 100   31 * 69 = 2139
32 + 68 = 100   32 * 68 = 2176
33 + 67 = 100   33 * 67 = 2211
34 + 66 = 100   34 * 66 = 2244
35 + 65 = 100   35 * 65 = 2275
36 + 64 = 100   36 * 64 = 2304
37 + 63 = 100   37 * 63 = 2331
38 + 62 = 100   38 * 62 = 2356
39 + 61 = 100   39 * 61 = 2379
40 + 60 = 100   40 * 60 = 2400
41 + 59 = 100   41 * 59 = 2419
42 + 58 = 100   42 * 58 = 2436
43 + 57 = 100   43 * 57 = 2451
44 + 56 = 100   44 * 56 = 2464
45 + 55 = 100   45 * 55 = 2475
46 + 54 = 100   46 * 54 = 2484
47 + 53 = 100   47 * 53 = 2491
48 + 52 = 100   48 * 52 = 2496
49 + 51 = 100   49 * 51 = 2499
50 + 50 = 100   50 * 50 = 2500
51 + 49 = 100   51 * 49 = 2499
52 + 48 = 100   52 * 48 = 2496
53 + 47 = 100   53 * 47 = 2491
54 + 46 = 100   54 * 46 = 2484
55 + 45 = 100   55 * 45 = 2475
56 + 44 = 100   56 * 44 = 2464
57 + 43 = 100   57 * 43 = 2451
58 + 42 = 100   58 * 42 = 2436
59 + 41 = 100   59 * 41 = 2419
60 + 40 = 100   60 * 40 = 2400
61 + 39 = 100   61 * 39 = 2379
62 + 38 = 100   62 * 38 = 2356
63 + 37 = 100   63 * 37 = 2331
64 + 36 = 100   64 * 36 = 2304
65 + 35 = 100   65 * 35 = 2275
66 + 34 = 100   66 * 34 = 2244
67 + 33 = 100   67 * 33 = 2211
68 + 32 = 100   68 * 32 = 2176
69 + 31 = 100   69 * 31 = 2139
70 + 30 = 100   70 * 30 = 2100
71 + 29 = 100   71 * 29 = 2059
72 + 28 = 100   72 * 28 = 2016
73 + 27 = 100   73 * 27 = 1971
74 + 26 = 100   74 * 26 = 1924
75 + 25 = 100   75 * 25 = 1875
76 + 24 = 100   76 * 24 = 1824
77 + 23 = 100   77 * 23 = 1771
78 + 22 = 100   78 * 22 = 1716
79 + 21 = 100   79 * 21 = 1659
80 + 20 = 100   80 * 20 = 1600
81 + 19 = 100   81 * 19 = 1539
82 + 18 = 100   82 * 18 = 1476
83 + 17 = 100   83 * 17 = 1411
84 + 16 = 100   84 * 16 = 1344
85 + 15 = 100   85 * 15 = 1275
86 + 14 = 100   86 * 14 = 1204
87 + 13 = 100   87 * 13 = 1131
88 + 12 = 100   88 * 12 = 1056
89 + 11 = 100   89 * 11 =  979
90 + 10 = 100   90 * 10 =  900
91 +  9 = 100   91 *  9 =  819
92 +  8 = 100   92 *  8 =  736
93 +  7 = 100   93 *  7 =  651
94 +  6 = 100   94 *  6 =  564
95 +  5 = 100   95 *  5 =  475
96 +  4 = 100   96 *  4 =  384
97 +  3 = 100   97 *  3 =  291
98 +  2 = 100   98 *  2 =  196
99 +  1 = 100   99 *  1 =   99

Press any key to continue . . .

Therefore, the maximum value of the product of two positive numbers whose sum is 100, is 2500

 

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