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# Linear Programming Project

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 of
the 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?