most profit? the price of each one of fruit (A) is 300 $ and price of each one of fuit (B) is 800 $ and we can sell them for 400 $ and 1000 $ we have 240 000 $ to buy fruit and we can buy 500 kilo(k) how we can have better profit? fruit (a) = buy 300 sell 400  profit = 100 fruit (b) buy 800 sell 1000 profit= 200 have 240 000 to buy 500 kilo fruit most profit?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Fruit A:

Profit per $1 of investment is `100/300=$1/3`

Also for $1 you can buy `1/300`kg

Fruit B:

Profit per $1 of investment is `200/800=$1/5`

Also for $1 you can buy `1/800`kg

So you need to maximize function `p`, that is profit, under certain conditions:

`p=1/3x_A+1/5x_B`                      (1)

`1/300x_A+1/800x_Bleq500`             (2)

`x+yleq240000`                       (3) 

`x,ygeq0`                                  (4)

(1) - profit from buying fruit A and B for `x_A` and `x_B` dollars respectivly.

(2) - this condition says we must buy 500kg of fruit

(3) - this condition says we must spend $240000

(4) - this condition says we can't spend negative amount of money

We need to maximize `p`. We can do that by looking what is the value of `p` in vertices of polygon given bx conditions (2)-(4). In other word we are looking the value of `p` in intersections of lines given by conditions (2)-(4).

This is usually done by simplex method but thic case is very simple so you can check all vertices. I will tell you that your solution at the intersection of coditions (2) and (3) so that means you need to buy

320kg (spend `x_A=$96000` ) and 180kg (spend `x_B=$144000` ) so your profit is `p=$60800`.

Fot more on linear programming see the links below or some literature e.g. Bertsimas D., Introduction to linear optimization.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial