Question

Problem 3. A fertilizer company blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $77.00 per pound. Fertilizer 2 must be at least 70% silicon and sells for $55.00 per pound. The company can purchase up to 8,000 pounds of nitrogen at $22.00 per pound and up to 10,000 pounds of silicon at $16.00 per pound. Assuming that all fertilizer produced can be sold, create a linear programming model to determine how the company can maximize its profit. Purchase costs Nitrogen Silicon Fertilizer 1 Fertilizer 2 Selling prices Minimum nitrogen in fertilizer 1 (%) Minimum silicon in fertilizer 2 (%) Available Blending plan (pounds of inputs into pounds of outputs) Fertilizer 1 Fertilizer 2 Nitrogen Silicon Total 0 0 Nitrogen constraint Actual Silicon constraint Actual >= Required Required Total cost Total revenue Profit

Answer 1

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Purchase wast $22 1 pound Netragen $ 16 / pound Silicon Feethlizen! $ 77 / pound fentligen 2 $ 55 / pound Selling prices 1) Sool Menimium nitrogen in fertilizer 70% 2 (0%) Selecon Blending plan Available fertilizer2 Feothliga 1 WOOD 8060 10000 4000 Natouagen Sehion 7000 800.00 71000 4000 Setuón constraint Nitrogen constraint 10000 Achiel 8000 Actual 7000 Required 4000 Required - 200000 Total cost 4000822 + 7000x 16 Total Revenue 4000 vn & 1000 x 55 - 693000 493000 : Natur Profit = 693000 - 200000