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The Sweet Smell Fertilizer Company markets bags of manure labeled “exactly 60 lb dry weight”. The packaged manure is a combination of compost and sewage wastes. To provide good quality fertilizer, each bag should contain at least 30 percent compost but no more than 40 percent sewage. Each pound of sewage cost Sweet Smell 5 cents and each pound of compost costs 6 cents. Formulate as a linear programming problem.

Consider the problem:

Minimize C = 3×1 + 4×2
Subject to:
6×1 + 5×2 ≥ 45
5×1 + 8×2 ≥ 60
x2 ≥ 2
and
x1, x2 ≥ 0

Solve, using the graphical technique of linear programming.