Question

Bullco blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 40% nitrogen and sells for $70/lb. Fertilizer 2 must be at least 70% silicon and sells for $40/lb. Bullco can purchase up to 80 lb of nitrogen at $15/lb and up to 100 lb of silicon at $10/lb. Assuming that all fertilizer produced can be sold, formulate an LP to help Bullco maximize profits.

Answer 1

To help Bullco maximize profits, a linear programming (LP) problem can be formulated. The problem involves producing two types of fertilizers, each with specific constraints on the percentage of nutrients and selling price, as well as limitations on the purchase of raw materials. By defining decision variables, an objective function, and constraints, the LP problem can be solved to determine the optimal production quantities that maximize profits.

Step-by-step explanation:

This problem can be solved using linear programming (LP) to maximize profits for Bullco. Let's define the decision variables:

• Let x be the amount of Fertilizer 1 produced, in pounds
• Let y be the amount of Fertilizer 2 produced, in pounds

The objective function to maximize profits is given by:

Z = 70x + 40y

The constraints for this problem are:

• The amount of nitrogen used in Fertilizer 1 must be at least 40% of the total weight of Fertilizer 1, so the constraint is: x >= 0.4x + 0.7y
• The amount of silicon used in Fertilizer 2 must be at least 70% of the total weight of Fertilizer 2, so the constraint is: y >= 0.7y + 1.8x
• Bullco can purchase up to 80 pounds of nitrogen at $15 per pound, so the constraint is: 0.4x + 0.7y <= 80
• Bullco can purchase up to 100 pounds of silicon at $10 per pound, so the constraint is: 0.7y + 1.8x <= 100

Finally, the non-negativity constraints are:

x >= 0

y >= 0

Now, you can solve this LP problem using linear programming techniques to find the values of x and y that maximize the profits for Bullco.