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
Profit per $1 of investment is `100/300=$1/3`
Also for $1 you can buy `1/300`kg
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:
(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.