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Question S. (22. points) A farmer owns 1,000 acres of more or less homogeneous farmland. His options are to breed cattle, or plant wheat, corn, or tomatoes. It takes four acres to support one head of cattle. Annually, 12,000 hours of labor are available. (For simplicity, assume that these 12,000 hours could be used at any time during the year, l.e., through hiring casual labor during seasons of high need, e.g., for harvesting). Table below provides information regarding the profit, yleld, and labor needs for the four economic activities. Table-Q4.1. Information table Furthermore, it is required that at least 20% of the farmland that is cultivated in the process must be used for the purpose of cattle breeding, at least 5% of the available farmland can be used for growing tomatoes and at least 15% of the available farmland can be used for growing corn. You are asked to determine the optimal amount of land allocated to each option that maximizes the total profit. You will formulate a linear programming model to determine the optimal solution using Excel Solver. NOTE: SHOW ALL YOUR WORK. a) (3 points) What are the decision variables? How many decision variables are there? Clearly explain the decision variables in English and provide the mathematical notation used in the algebraic formulation of the decision problem. b) (2 points) What is the objective function? Clearly explain the objective function in English and provide the mathematical formulation. c) (6 points) What are the constraints of the problem? Clearly explain each constraint in English and provide the mathematical formulation. d) (1 points) Are there any sign or type restrictions in your formulation? Why or why not? Clearly explain the sign and type restrictions (if any). e) Prepare a spreadsheet to determine the optimal production plan using Excel Solver. i. (2 points) Provide a screenshot of your spreadsheet model. The screenshot should show all the cells involved in formulating the optimization problem. NOTE: DO not copy and paste your spreadsheet to your answer report as an Excel object. Instead, capture a screenshot in Excel and paste this as an image. ii. (2 points) Provide a screenshot of your spreadsheet with the formula view. You can switch from normal view to formula view in Excel by clicking the CTRL and keys on your keyboard simultaneously. iii. (2 points) Prepare the Solver model by logging all the information to the Solver Parameters window in Excel. Provide a screenshot of the Solver Parameters window in Excel. Iv. (2 points) Finally, solve the optimization problem using the Simplex LP method in Excel Solver. What is the optimal solution, i.e., the optimal values of the objective function and the decision variables? f) ( 2 points) Report the capacity utilization of the farmland