Question

the farmer needs to plant at least 3 acres of rye, but no more than 15 acres of rye. the farmer needs to plant at least 1 acre of wheat, but no more than 7 acres of wheat. the farmer has up to 20 acres available for planting wheat and rye. each acre of wheat makes a profit of #500.Each acre of rye makes a profit of $300.
Write the constraints for this situation

Answer 1

let 
x = acres of when 
y = acres of rye 

Maximize 
z = 500x + 300y 

subject to 
x >= 3 
x <= 15 
y >= 1 
y <= 7 
x + y <= 20 

bounded 

both 

(3, 1) 
(15, 1) 
(15, 5) 
(13, 7) 
(7, 3) 

sub points into your max equation 
(3, 1) = 1500 + 300 = 1800 
(15, 1) = 7500 + 300 = 7800 
(15, 5) = 7500 + 1500 = 9000 
(13, 7) = 6500 + 2100 = 8600 
(7, 3) = 3500 + 900 = 4400 

max profit of $9,000 is achieved when 15 acres of wheat and 5 acres of rye are planted and sold