The Sweet Smell Fertilizer Company markets bags of manure labeled$$ "not less than lb dry$$ weight." The packaged manure is a combination of compost and sewage wastes. To provide$$ good$-$quality fertilizer, each bag should contain at least lb of compost but no more than lb of sewage. Each pound of compost costs Sweet Smell $$ and each pound of sewage costs $.$

You have been asked to develop a linear programming model so as to minimize the total cost of producing a bag of$$ fertilizer, with two decision$$ variables: $(1)$ number of pounds of compost in each$$ bag, and$(2)$ number of pounds of sewage waste in each bag.