Question

Maxima and minina...

1.) The sum of one number and two times a second number is 24. What numbers should be selected so that their product is as large as possible?

Answer 1

the numbers are 12 and 6....

Answer 2

use x+2y=24
and then use p=xy
use x=24-2y in 2nd eqn
differentiate it wrt y and for max or min p' should be zero so y =6 and x= 12

Answer 3

U have x+2y=14 so maybe multiply through by x gives x^2+2yx =14x ->yx=12x -x^2/2

Treating yx as some f(x) and differentiate 12-x = 0 for max x=12 giving a product of 72 (cf x= 10, product 70 or x=14, product 70)

Not entirely sure about the mathematical legitimacy of this...