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.

Question

anonymous · Answer

I have noo idea how to even start that.

amistre64 · Answer

let the numbers be a and b

a + 4b = 1000

ab is a max

amistre64 · Answer

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

amistre64 · Answer

or you could play with langrange multipliers ...

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

Thank you!