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,what is the amount of nitrogen from the Nitro Plus brand?
A)11.45
B)12.80
C)17.65
D)11.55

Question

Quizplus · Accepted Answer

Let x be the number of bags of Nitro Plus and y be the number of bags of Phosphate Max. 
We want to maximize the amount of nitrogen from Nitro Plus: 
Maximize: 8x 
Subject to: 
6x + 8y ≥ 48 (phosphate constraint) 
8x + 4y ≥ 32 (nitrogen constraint) 
x, y ≥ 0 (non-negativity constraint)

We can plot these constraints on a graph and find the intersection point that maximizes 8x:

- phosphate constraint: y ≥ -3/4x + 6 
- nitrogen constraint: y ≥ -2x + 8

The intersection point is at (3, 3), which means John should buy 3 bags of Nitro Plus and 3 bags of Phosphate Max. 
The amount of nitrogen from Nitro Plus is 8x = 8(3) = 24 pounds.

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