In: Math
A company is creating a new fertilizer additive for lawn seed, which will be a mixture of nitrogen, phosphate, and potash. Based on their research, the total amount fertilizer added must be at least 14 oz. per 5 lb. bag of lawn seed, but should not exceed 20 oz. per 5 lb. bag. At least ¼ oz. of nitrogen must be used for every ounce of phosphate, and at least 1 oz. of potash must be used for every ounce of nitrogen. The costs per ounce of nitrogen, phosphate, and potash are $0.30, $0.18, and $0.54, respectively. Determine the mixture of the three ingredients in a 5 lb. bag that minimizes costs, as well as that cost.