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maxi product

maxi product The objective of this coursework is to find the formula that gives the maximum product of any given number when split into parts. For the first part of the coursework I am going to investigate the splitting of a number into two parts, then three parts and into four and five parts. For each number of parts, I am going to come up with a formula that gives the maximum product. PAIR WHICH TOTAL 12 PRODUCT OF THE PAIR I will assume my maxi product is in the range between 7,5 and 5,7 because this where the arch is at it’s highest. So, Neither of these are higher than 36. So for my starting number 12, I have used the pairs 6 and 6 and my maxi product is 36. PAIR WHICH TOTAL 10 PRODUCT OF THE PAIR Again, I am looking in the range between 6,4 and 4,6. Neither of the products are higher than 25. For my starting number 10, I have used the pair 5,5 and my maxi product is 25. PAIR WHICH TOTAL 14 PRODUCT OF THE PAIR Between 8,6 and 6,8 as this is where the number is highest. For my starting number 14, I have used 7,7 and my maxi product is 49. PAIR WHICH TOTAL 16 PRODUCT OF THE PAIR Between 9,7 and 7,9 as this is where the number seems highest. For my starting number 16, I have used the pair 8,8 and my maxi product is 64. PAIR WHICH TOTAL 9 PRODUCT OF THE PAIR The maxi product lies somewhere between 5,4 and 4,5. 20.25 is the highest, therefore my maxi product is 20.25. The pair I used was 4.5 and 4.5. PAIR WHICH TOTAL 13 PRODUCT OF THE PAIR The maxi product is somewhere between 7,6 and 6,7. For my starting number 13, my maxi product is 42.25. The pair I have used is 6.5 and 6.5. STARTING NUMBERS PAIR WHICH GIVE MAXIPRODUCT VALUE OF MAXI PRODUCT By investigating these numbers and their results, I have come up with a formula for finding the maxi product of any given number. Let the starting number be m and n represent 2 The formula would then be (m/n)ⁿ For this part of the coursework I am going to investigate the maxi product of numbers split into triples. I will ignore numbers that contain the number zero, apart from the combination, which includes the starting number. TRIPLE NUMBERS WHICH TOTAL 12 PRODUCT I will test for the maximum product between 5,3,4 and 3,4,5. I have not found any numbers higher than 64, therefore 64 is my maximum product. TRIPLE NUMBERS WHICH TOTAL 9 PRODUCT 24 seems to be the highest product as the following has begun to decrease in value. However, there might be fractions that may be larger. Not higher so 27 is definitely my maxi product. TRIPLE NUMBERS WHICH TOTAL 15 PRODUCT In my test for the maximum product I will use a combination that has not been used in the table. This is bigger than the highest number in the table. So I will use 125 as my maxi product. TRIPLE NUMBERS THAT TOTAL 18 PRODUCT Because I have looked on the results of the previous tables I am going to assume my maxi product is Starting numbers Triple numbers which give maxi product Value of maxi product m again represents the starting number and n represents 3 because the starting number was split into three parts. This part observes the number split into quadruples. Again, I have to come up with a formula that represents the maxi product of a number split into quadruples. 81 looks to be the highest in the table, however I will check This is not the maxi product it is too low. This is the maximum product as it is the highest. I am going to try a different combination STARTING NUMBERS QUADRUPLES THAT GIVE MP VALUE OF THEMAXI PRODUCT Bibliography:

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