Linear Programming homework

Due Wednesday, October 23rd (for MRS21-3) or Thursday, October 24th (for MRS21-1)
Cats need these nutrients to survive: amino acids, fatty acids, carbohydrates, vitamins, minerals, and water. Mr. Bean wants to provide his adult cat, Teddy a healthy diet but wants to minimize his cost as he gives Teddy two different brands of food per day. Teddy prefers to eat at most twice of Brand A as compared to Brand B. The veterinarian has recommended that Teddy needs at most 15 grams of crude protein and at least 0.5 gram of mineral per day. Food brand A provides 2.5 gram of crude protein and 0.05 gram of mineral per serving and Brand B provides 3 grams of crude protein and 0.15 gram of mineral per cup.
How many cups of each type of brand should Mr. Bean buy in order to minimize his costs if a cup of Brand A cost 110¢ per cup and Brand B cost 175¢ per cup? How much is the minimum
Mr. Bean later found out that Retail shop XYZ sells these brands at a cheaper price if he buys it in bulks. How much extra can Mr. Bean save if brand A and B is 8% and 4.5% cheaper, respectively? Explain.

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