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