Ross White recently opened a landscaping division , that advises home owners and businesses on landscaping and lawn maintenance. The operations manager, Ms. Priya Johnson, is trying to determine the amount of fertilizer that should be applied to a particular lawn in a residential area in San Juan. Ms. Johnson’s analysis has determined that the lawn needs at least 60kg of Nitrogen, 24kg of Phosphorous compounds and 40kg of Potassium compounds for the current season. After checking nearby home and garden centres, Ms. Johnson has found that one of the suppliers is currently having a sale on packaged fertilizer. One type on sale called Xynis, is a 20-5-20 mixture, containing 20% Nitrogen, 5% phosphorous compounds and 20% potassium compounds. It sells at $4 for a 20kg bag. The other type called Yield-all is a 10-10-5 mixture (10% Nitrogen, 10% phosphorous compounds and 5% potassium compounds) selling for $5 for a 40kg bag. Ms. Johnson would like to know how many bags of each type she should purchase so that she can combine the ingredients that will at least meet the minimum nutrient requirements for the lawn. As any conscientious manager owner, Ms. Johnson wishes to spend as little as possible. Assuming that she wishes to use a combination of the two fertilizers in order to supply at least the recommended nutrient levels at minimum cost, express this information as a linear programming problem.
Ross White recently opened a landscaping division , that advises home owners and businesses on landscaping and lawn maintenance. The operations manager, Ms. Priya Johnson, is trying to determine the amount of fertilizer that should be applied to a particular lawn in a residential area in San Juan.
Ms. Johnson’s analysis has determined that the lawn needs at least 60kg of Nitrogen, 24kg of Phosphorous compounds and 40kg of Potassium compounds for the current season. After checking nearby home and garden centres, Ms. Johnson has found that one of the suppliers is currently having a sale on packaged fertilizer.
One type on sale called Xynis, is a 20-5-20 mixture, containing 20% Nitrogen, 5% phosphorous compounds and 20% potassium compounds. It sells at $4 for a 20kg bag. The other type called Yield-all is a 10-10-5 mixture (10% Nitrogen, 10% phosphorous compounds and 5% potassium compounds) selling for $5 for a 40kg bag.
Ms. Johnson would like to know how many bags of each type she should purchase so that she can combine the ingredients that will at least meet the minimum nutrient requirements for the lawn. As any conscientious manager owner, Ms. Johnson wishes to spend as little as possible.
- Assuming that she wishes to use a combination of the two fertilizers in order to supply at least the recommended nutrient levels at minimum cost, express this information as a linear programming problem.
Step by step
Solved in 3 steps
