In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,the total fertilizer costs are ______.
A)$29.80
B)$54.40
C)$76.25
D)$80.00

Question

Quizplus · Accepted Answer

To minimize costs while meeting the nitrogen and phosphate requirements, we can set up and solve a linear programming problem. Let x be the number of Nitro Plus bags and y be the number of Phosphate Max bags. The objective is to minimize the cost C = 7x + 9y subject to the constraints: 8x + 4y ≥ 32 (nitrogen requirement) and 6x + 8y ≥ 48 (phosphate requirement). Solving this system, we find that the optimal solution involves buying a combination of Nitro Plus and Phosphate Max bags that minimizes the total cost while meeting the requirements. The correct total cost at the optimal solution is $54.40, indicating that the combination of fertilizers chosen meets the minimum requirements for nitrogen and phosphate at the lowest possible cost.

In Order to Fertilize His Vegetable Farm,John,a Farmer,needs to Choose