Question

A company supplies fertilizers to its customers on a make-to-order basis by blending appropriate amounts of “stock” fertilizers. These stock fertilizers are purchased direct from a factory in 100 lb. bags and either a whole bag or a part of it can be used in the final blend. Customer orders are specified as a triple of percentages N-P-K where N, P and K are (respectively) the minimum desired percentages of nitrogen, phosphorus and potassium in the fertilizer. An order has just been received for 1000 lbs of 17-14-10 fertilizer: the customer wants at least 17% of the fertilizer’s weight to be nitrogen, at least 14% to be phosphorus and at least 10% to be potassium. There are three “stock” fertilizer types and the company will use a total of ten 100-lb bags of these to fill this order: Type 1 is a 50-20-5 fertilizer, Type 2 is a 0-15-20 fertilizer and Type 3 is a 10-10-10 fertilizer (for stock fertilizers N-P-K values represent exact percentage compositions in the 100 lb. bag). The costs of a 100 lb. bag of Type 1, Type 2 and Type 3 are $90, $20 and $30 respectively. Formulate a linear program to come up with the least expensive way to satisfy the order.

Answer 1