Based on Angel et al. (2003). A fertilizer company is trying to determine the cheapest fertilizer mix that provides desired amounts of nutrients. The mix is made by combining the following fertilizers: SSA, SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage of potassium (K), sulfur (S), calcium (Ca), sodium (Na) and phosphorus (P) in each fertilizer is listed in the file P06_88.xlsx. For example, a pound of SSA is 16% K and 26% Na. The mix must contain at least 600 pounds of K, 550 pounds of S, 750 pounds of Ca, 900 pounds of Na, and 750 pounds of P. The mix cannot contain both GUR and TSP, because if both are present in the mix, the affect of other fertilizers is nullified. The cost per pound (in cents) of each fertilizer is listed in the same file. Develop a linear integer model to find the minimum-cost fertilizer mixture that meets the stated chemical requirements.
Based on Angel et al. (2003). A fertilizer company
is trying to determine the cheapest fertilizer mix that
provides desired amounts of nutrients. The mix is
made by combining the following fertilizers: SSA,
SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage of
potassium (K), sulfur (S), calcium (Ca), sodium (Na)
and phosphorus (P) in each fertilizer is listed in the file
P06_88.xlsx. For example, a pound of SSA is 16% K
and 26% Na. The mix must contain at least 600 pounds
of K, 550 pounds of S, 750 pounds of Ca, 900 pounds
of Na, and 750 pounds of P. The mix cannot contain
both GUR and TSP, because if both are present in the
mix, the affect of other fertilizers is nullified. The cost
per pound (in cents) of each fertilizer is listed in the
same file. Develop a linear integer model to find the
minimum-cost fertilizer mixture that meets the stated
chemical requirements.
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