Question

%*I need help solving this problem

Question is: How many acres of apple trees and how many acres of orange trees will they plant in order to receive the maximum profit? What is the maximum profit?

*There are social workers who are planning to plant some apple trees and orange trees on a land of 50 acres. *The land planted with apple trees requires 5 workers per acre and 5 tons of fertilizer per acre. It will yield a $500 profit per acre. *The land planted with orange trees requires 4 workers per acre and 7 tons of fertilizer per acre. It will yield $600 profit per acre. Currently, there are 150 workers and 200 tons of fertilizer available

Answer 1

The given question can be solved using Linear Programming Problem (LPP).

Let x be percentage of land allotted for Apples and

Let y be percentage of land allotted for Oranges

• Profit per acre of land of apple is 500$ and orange is 600 $. So Total Profit => 500x + 600y ..(1)
• Per acre land of apple requires 5 workers and orange requires 6. Total available workers are 150. So equation is 5x + 4y ≤ 150 ...(2)
• Per acre land of apple requires 5 tons and orange requires 7. Total available workers are 200. So equation is 5x + 7y ≤ 200 ...(3)

Hence the LPP equation is to,

Maximise Z = 500x + 600 y

subject to,

5x + 4y ≤ 150

5x + 7y ≤ 200

x,y > = 0

So we solve above:

5x + 4y = 150

5x + 7y = 200

Solving above we get Y = 16.67 and X = 16.67.

Hence , Ratio of x ; y = 16.67 ; 16.67 or 1 : 1.

So total available land is 50 acres. It should be distributed equally ie 25 acres for Apple and 25 Acres for Orange.