1. Farmer Fugua has 90 acres on which she may raise cotton and soybeans. She has accepted orders requiring at least 10 acres of cotton and 5 acres of soybeans. She also must follow a regulation that the acreage for soybeans must be at least twice the acreage for cotton. If the profit is $100 per acre of soybeans and $200 per acre of cotton, how many acres of each will give her the greatest profit?

Question

1.	Farmer Fugua has 90 acres on which she may raise cotton and soybeans.  She has accepted orders requiring at least 10 acres of cotton and 5 acres of soybeans.  She also must follow a regulation that the acreage for soybeans must be at least twice the acreage for cotton.  If the profit is $100 per acre of soybeans and $200 per acre of cotton, how many acres of each will give her the greatest profit?

anonymous · Answer

this is linear programming

anonymous · Answer

let there be 
$x$ acres of cotton
and $y$ acres of soybean

total area is:  $x+y\le90$
condition that :$y\ge2x$
profit:  $p=100x+200y$

anonymous · Answer

we graph the first two inequalities.

anonymous · Answer

what happened to the 10 and 5

anonymous · Answer

oh yes.
$$x\ge10\y\ge5$$

anonymous · Answer

why is it just x>10 why is it not X+y>10

anonymous · Answer

because
x+y = sum of areas of cotton and soybean and that is a different inequality

anonymous · Answer

ok gotcha

anonymous · Answer

:)

anonymous · Answer

ok going to work it out and come back