You are an undergraduate student who studies linear programming in your quantitative methods course. Your parents run an agriculture business and they manage 80 acres of farm land. The firm plants maize crop and vegetables on the farm. The firm earns a net profit of 5,000$ for each acre planted with maize crop and 3,000$ for every acre of land planted with vegetables. The firm has to comply with the government environmental protection agency (EPA) regulations. The regulations restrict the firm’s total pesticide usage to 100 gallons for the entire 100 acres farm. Maize plantation requires 2 gallons of pesticide per acre while every acre plantation of vegetables require 1 gallon. Your parents have asked you to help them optimize their business operations by answering the following questions.

A) Formulate a linear programming problem by writing the following

- Objective function of the firm

- Constraints on the firm

- Non-negativity constraints

B) What combination (acres of maize, acres of vegetable) should the firmplant in order to maximize the net profit?

C) What would be the optimized net profit of the firm?