# Math Help - optimization problem #4

1. ## optimization problem #4

Hi I need help doing this question.

Compute the max product for two positive numbers with the property that the sum of the first plus five times the second is 5000.

Can anyone do this problem? thanks

2. Originally Posted by mike21
Hi I need help doing this question.

Compute the max product for two positive numbers with the property that the sum of the first plus five times the second is 5000.

Can anyone do this problem? thanks
let $x$ = the first (+)number

$y$ = the second

the sum of the first plus five times the second is 5000.

$x+5y = 5000$

$x = 5000-5y$

product ... $P = xy = (5000-5y)y$

determine $P_{max}$ using the method taught to you in class