+16 A farmer has 1,300 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $69,500 for the cost of growing his crops. How many acres of each crop should he plant?
+37084 Let c = corn acres cost = 45c
let w = wheat acres = 2c (given) cost = 60(2c) = 120c
let s = soybean acres = 1300 acres - corn acres - wheat acres = 1300 - c - 2c cost = (50)(1300-3c)
All three of these costs added together = 69500 = 45c +120c + 50(1300-3c) Now solve for 'c'
You should result in :
c = 300 acres
then
w = 2c = 600 acres
and
s = 1300 - corn - wheat = 1300 - 300 - 600 = 400 acres for wheat
