Please answer the question with explainning the steps. Thanks! Each year a farme

Question

Please answer the question with explainning the steps. Thanks!

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 each 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 $ 66. Formulate

the farmer's decision problem as a Linear Programming problem by identifying the choice

variables, the objective function and the constraints.

Explanation / Answer

Let G be the acres of grain used, and V be the acres of vegetables used. Then we want to maximize profit, which is equal to P(G,V) = 50G + 66V. The constraints correpond to the limited amount of land, machine hours, and labor, so they are:

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