Question

Each year a farmer has 100 acres of land, 3880 machine hours and 2500 labor hours to grow grain and vegetables. Each acre of grain requires 15 labor hours and 40 machine hours per year, while eaxch acre of vegetables needs 35 labor hours and 25 machine hours per year. The profit per acre of grain is $ 50, and that per acre of vegetables is $68. Formulate the farmer's decision problem by following the WWW procedure discussed in class. In other words, you need to identify the choice variables (what you can do), the objective function (what you want), and the constraints (what you can NOT do).

Note: This is a Linear Programming (LP) problem because all functions are linear. If any of the obtained objective or constraint functions are non-linear, it will be called non-linear programming; if any of the involved choice variables are integers, it will be called integer programming.

Answer 1

acres of gerain acres n Assume i to be the used & let v be the of vegetables wed we wan to matinize pewfit , which is equal to to Pla, v)=506+ 68 v The constraints Correspond to an land machne hours & labor; am they 15h +35v <= 25 o o the linnited c su you + 250 <=3880 at v C = 100