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 four Parts. For each number of parts, This will result with a formula that gives the maximum product. Pairs Starting number 12, PAIRS WHICH TOTAL 12 & PRODUCT OF THE PAIR 12,0 = 0 11,1 = 11 10,2 = 20 9,3 = 27 8,4 = 32 7,5 = 35 6,6 = 36 5,7 = 35 4,8 = 32 3,9 = 27 10 = 20 1,11 = 11 0,12 = 0 …

…as it is the highest. Starting number 14 QUADRUPLES WHICH TOTAL 14 & PRODUCT 14,0,0,0 =0 11,1,1,1 =11 10,1,1,2 =20 9,1,2,2 =36 8,2,2,2 =64 7,2,4,1 =56 6,6,1,1 =36 5,4,4,1 =80 4,4,4,2 =128 3,4,6,1 =72 2,3,3,6 =108 TEST FOR THE MAXI PRODUCT 3.75 x 3.25 x 3 x 4= 146.25 I am going to try a different combination 3.5 x 3.5 x 3.5 x 3.5=150.06 That is the maxi product. STARTING NUMBERS QUADRUPLES THAT GIVE MAXI PRODUCT VALUE 12, 3x 3 x 3 x3 =81 16, 4 x 4 x 4 x 4 =256 14, 3.5 x 3.5 x 3.5 x 3.5 =150.06 M= n/4 x n/4 x n/4 x n/4 = (¨ù)4 M again represents the Maxi Product and n represents the Starting number. The formula is (¨ù)3 .