A farmer owns 45 acres of land, which she plans to plant with either wheat or corn. Each acre of wheat yields $200 in prot and each acre of corn yields $300 in prot. The labor and fertilizer requirements for each acre of wheat are 3 workers and 2 tons of fertilizer while for each acre of corn 2 workers and 4 tons of fertilizer are needed. Suppose that 100 workers and 130 tons of fertilizer are available all together, how many acres should she plant for each crop in order to maximize the total prot? Solution Let W denote wheat fields and C denote corn fields. 45 = W + C 100 = 3W + 2C , since we have 100 workers and 3 are required for wheat and 2 for corn. 130 = 2W + 4C, since we have 130 tons and 2 are required for wheat and 4 for corn. Solve the system of equations ... 100 = 3W + 2C - 130 = 2W + 4C - 45 = 1W + 1C ------------------------------- -75 = -3C C = 25 So plug 25 back into the equation 45 = 1W + 1C 45 = 1W + 25 W = 20 Plant 25 acres of corn and 20 acres of wheat. .

1. A farmer owns 45 acres of land, which she plans to plant with either wheat or
corn. Each acre of wheat yields $200 in prot and each acre of corn yields $300 in prot.
The labor and fertilizer requirements for each acre of wheat are 3 workers and 2 tons of
fertilizer while for each acre of corn 2 workers and 4 tons of fertilizer are needed. Suppose
that 100 workers and 130 tons of fertilizer are available all together, how many acres should
she plant for each crop in order to maximize the total prot?
Solution
Let W denote wheat fields and C denote corn fields. 45 = W + C 100 = 3W + 2C , since we have
100 workers and 3 are required for wheat and 2 for corn. 130 = 2W + 4C, since we have 130 tons
and 2 are required for wheat and 4 for corn. Solve the system of equations ... 100 = 3W + 2C -
130 = 2W + 4C - 45 = 1W + 1C ------------------------------- -75 = -3C C = 25 So plug 25 back
into the equation 45 = 1W + 1C 45 = 1W + 25 W = 20 Plant 25 acres of corn and 20 acres of
wheat.