A lawn and garden store creates three different potting mixes sold in 20-pound b

Question

A lawn and garden store creates three different potting mixes sold in 20-pound bags. Mix A contains 12 pounds of peat, 5 pounds of perlite, 3 pounds of organic material, and earns a profit of $4 per 20-pound bag. Mix B contains 10 pounds of peat, 6 pounds of perlite, 4 pounds of organic material, and earns a profit of $5 per bag. Mix C contains 8 pounds of peat, 8 pounds of perlite, 4 pounds of organic material, and earns a profit of $6 per bag. There are 1, 264 pounds of peat, 880 pounds of perlite, and 640 pounds of organic material available every week to make these potting mixes. How many 20-pound bags of each mix should be made in order to maximize weekly profit? bags of mix A, bags of mix B and bags of mix C.

Explanation / Answer

Let x bags of A and y bags of B and z bags of C are taken:

Total Peats: 1264 lb

12x +10y +8z <= 1264

Total Perlite: 880 lb

5x +6y +8z <= 880

Total Organic material: 640 lb

3x +4y +4z <= 640

x>=0 ; y>=0 ; z>=0

profit function is

P = 4x + 5y + 6z

Optimal solution of above system : : p = 708; x = 0, y = 96, z = 38

A = 0 bags ; B = 96 bags ; C = 38 bags

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