How many 20-pound bags of each mix should be packaged in order to maximize weekly profit

A landscape supply company packages three different soil mixes sold in 20-pound bags. Mix A contains 12 pounds of peat, 5 pounds of perlite, and 3 pounds of organic material. Mix A earns a profit of $3 per 20-pound bag. Mix B contains 10 pounds of peat, 6 pounds of perlite, and 4 pounds of organic material. Mix B earns a profit of $5 per 20-pound bag. Mix C contains 8 pounds of peat, 8 pounds of perlite, and 4 pounds of organic material. Mix C earns a profit of $6 per 20-pound bag. Each week the company has 1200 pounds of peat, 800 pounds of perlite, and 600 pounds of organic material available. How many 20-pound bags of each mix should be packaged in order to maximize weekly profit?

a) Clearly identify your variables

b) Set up the objective function

c) Determine the constraints

d) Setup the initial simplex tableau

e) Apply the simplex method, showing all the steps in the process, until a optimal solution is obtained.

f) Report your complete solution in terms of the number of bags of each mix and the maximum weekly profit.

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