Bartlett's Greenhouse produces two types of specialty fertilizers one for roses and the other for tomatoes. The three main ingredients in both fertilizers are Nitrogen, Phosphorus, and Potassium. Fertilizers are sold in bags. A 1 kilo bag of rose fertilizer contains 200 grams of Nitrogen, 120 grams of Phosphorus, and 80 grams of Potassium. A bag of tomato fertilizer contains 240 grams of Nitrogen, 70 grams of Phosphorus, and 90 grams of Potassium. They have 100 kilograms of a Nitrogen compound, 60 kilograms of a Phosphorus compound, and 50 kilograms of a Potassium compound available for use.
Bartlett's Greenhouse earns a profit of $3.00 for each bag of rose fertilizer it sells and $2.00 for each bag of tomato fertilizer it sells. Experience tells them that they can sell all of the fertilizer they produce but they would like to produce at least 75 bags of each type so customers have a choice.
a) Formulate an LP to maximize their profit. (Define decision variables and write the objective function and the constraints).
b) Build a spreadsheet model.