Thread: optimization problem

not quite understanding this question
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find 2 positive numbers that satisfy the given requirements
1.) the sum of the first number and twice the second number is 108 and the product if a maximum


well....to me it seems as if i will be working with this equation
a+2b=108

a = 108-2b
put equation into all one term... i picked a

so.. 108-2b+2b=108
turns this into
108=108
rofl and no im lost how am i suppose to work this?

Originally Posted by nuclear123

not quite understanding this question
------------------------------------
find 2 positive numbers that satisfy the given requirements
1.) the sum of the first number and twice the second number is 108 and the product if a maximum

$\displaystyle a+2b = 108$

let $\displaystyle P$ be the product ...

$\displaystyle P = ab = (108-2b)b$

find the value of $\displaystyle b$ that maximizes $\displaystyle P$