Question

Calculus: Find two numbers where the sum of the first number and four times the second number is 1000, and the product of both is as large as possible.

Answer 1

I have noo idea how to even start that.

Answer 2

let the numbers be a and b

a + 4b = 1000

ab is a max

Answer 3

define a or b in terms of the other and work out a quadratic to play with

Answer 4

or you could play with langrange multipliers ...

Answer 5

@amistre64 I got A as 500 and B as 125, does that sound right to you?

Answer 6

maybe ...

a + 4b = 1000; a = 1000-4b

ab = (1000-4b)b = 1000b - 4b^2

the vertex is at: b = -1000/-2(4) = 125

so yes

Answer 7

Thank you!