Mathematical Programming - Economic Development - Graphical - Economic Assessment Answer

Assessment Task:

Mathematical Programming - Economic Development - Graphical - Economic Assessment Answer 

Introduction
Decision-makers in natural resource management can be a complex process where the planner needs to balance multiple, and often competing, demands for resources.  For example desire to protect ecosystems, pressures of increased economic development, concerns over threatened species, exploitation of resources, and values for recreation and scenic landscapes.  Decision support tools are computer models that can help planners to evaluate the impacts of alternative management decisions. 
In the lectures and computer labs, you were introduced to mathematical programming. These techniques are widely used to construct decision support tools in ‘real-life’ natural resource management

Question 1a: tate the problem as a mathematical programming problem (objective function, constraints and non-negativity).  Find the optimal solution using Solver and give the optimal solution in a table.
Question 1b: 
Represent the graphical solution to the problem in a diagram.  Include all constraints and the isoprofit line for the optimal solution. The diagram should identify the feasible set, possible optimal solutions and the optimal solution. The diagram should be fully labelled and discussed in a comment.
Question 1c: 
Give the Lagrangean multipliers (shadow prices) for all three constraints and interpret each intuitively. The farmer can rent land at $0.7 (thousand per ha).  Would you advise Mary to rent more land or not.  How much should she rent if her other resources and constraints are fixed? (Hint: How do the Lagrange multipliers change as the land area is increased.)
Question 1d: 
Over what range of wheat profit does the optimal solution (in terms of the area of wheat and barley) remain constant (Hint find out about LP sensitivity analysis). Linear programming generates sensitivity analysis solutions automatically, explain the property of LP that makes this possible. 

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