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 phosphate from the Phosphate Max brand?
A)23.20
B)38.40
C)17.65
D)15.80

Question

Quizplus · Accepted Answer

Let x be the number of bags of Nitro Plus and y be the number of bags of Phosphate Max. 
The objective is to minimize the cost (7x + 9y). 
The constraints are: 
8x + 4y ≥ 32 (minimum nitrogen required) 
6x + 8y ≥ 48 (minimum phosphate required) 
x, y ≥ 0 (cannot have negative bags)

Solving these constraints, we get the optimal solution as x = 4 and y = 4.8 (can have a fraction of bags) 
The amount of phosphate from Phosphate Max brand is 8 × 4.8 = 38.40 
Therefore, the best choice is to buy 4 bags of Nitro Plus and 4.8 bags of Phosphate Max for a total cost of $69.60.

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