Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible

The first one is 198.4 and the second one is 801.6 

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)