Linear Programming Project

In this Project, each team will be provided with a linear programming problem that must be solved in detail. The solution to the problem must include the items listed below in a clear and orderly format. Once the team is certain that the solution is correct and complete, the solution should be submitted to the Instructor by the Due Date. Submissions after the Due Date will receive Lateness Deductions at the rate of 10% per calendar day late; the timestamp ofthe submission will be used in any such evaluation.

The following items must be clearly presented in the problems analysis and solution:

* The definition of all variables;
* A statement of the objective function;
* A listing of all the constraint inequalities;
* A graph showing the inequalities and the coordinates of the vertices;
* An evaluation of the objective function at each vertex;
* The conclusions drawn from the analysis.

Johnson's Produce is purchasing fertilizer with two nutrients: N (nitrogen) and P (phosphorus). They need at least 180 units of N and 90 units of P. Their supplier has two brands of fertilizer for them to buy. Brand A costs $10 a bag and has 4 units of N and 1 unit of P. Brand B costs $5 a bag and has 1 unit of each nutrient. Johnson's Produce can pay at most $800 for the fertilizer. How many bags of each brand should be purchased to minimize the cost? What is the minimum cost?