A farmer needs to determine how many acres of her property to plant with soybeans and how emany acres to plant with corn. An acre of soybeans requires 5 hours of labor per week and yields $120 in profit. An acre of corn yields $325 in profit and requires 8 hours of labor per week. The farmer has avail- able 14 acres of land and 40 hours per week of labor. Due to regulations that are part of the government's agricultural subsidy program, the farmer must plant no more than 8 acres of soybeans. Formulate, but DO NOT SOLVE, a linear program, the solution of which would tell the farmer how to maximize the total profit from soybeans and corn. In your formulation: (1) Clearly specify the variables; (2) Give the objective function and specify whether the objective is maximize or minimize; (3) List all the constraints

A farmer needs to determine how many acres of her property to plant with soybeans and how emany acres to plant with corn. An acre of soybeans requires 5 hours of labor per week and yields $120 in profit. An acre of corn yields $325 in profit and requires 8 hours of labor per week. The farmer has avail- able 14 acres of land and 40 hours per week of labor. Due to regulations that are part of the government's agricultural subsidy program, the farmer must plant no more than 8 acres of soybeans. Formulate, but DO NOT SOLVE, a linear program, the solution of which would tell the farmer how to maximize the total profit from soybeans and corn. In your formulation: (1) Clearly specify the variables; (2) Give the objective function and specify whether the objective is maximize or minimize; (3) List all the constraints.