Find two positive numbers whose product is 16 such that the sum of the first plus 4 times the second is a minimum. The two numbers are (enter the numbers separated by commas, e.g., "2,8")

Answer 1

xy = 16

x+4y is minimum

if the condition were x+y = minimum then (4,4) or x=y=4 would be the answer

by making it 4y you want x to be 4 times y or 4y+4y = 8y = minimum

xy=16

4y(y) = 16

y^2 = 16/4 = 4

y = 2, x=16/2 =8

(8,2)

2(8) = 16

8 + 4(2) = 16 the minimum value of x+4y, x=8, y=2

x=1, y=16 gives x+4y = 65

x=2, y=8 gives 2+32 = 34

x=4, y= 4 gives 4+16 = 20

x=8 y=2 gives 8+8 = 16

x=16 y=1 gives 16+2 = 18

x=9, y=16/9 gives 9+64/9 = 145/9 = 16.111....

x=7, y =16/7 gives 7+64/7 = 113/7= 16 1/7

(8,2) gives the minimum value of x+4y when xy=16