Question

Use the graphical method to solve each of the following LP problems.
A wheat and barley farmer has $168$ hectare of ploughed land, and a capital of $E2000$. It costs $E14$ to sow hectare wheat ad $E10$ to sow one hectare of barley.

Suppose that his profit is $E80$ per hectare of wheat and $E55$ per hectare of barley. Find the optimal number of hectares of wheat and barley that must be ploughed in order to maximise profit? What is the maximum profit?

Answer 1

assume that $x$ is wheat and $y$ is barley hectaters to maximum the profit

by question given that to convert in mathematically form

$x\times 14+10\times y\le 2000$

profit

$Z=80\times x+55y$

and $x+y\le 168$

$x\le 0$

$y\le 0$

$7x+5y\le 1000$

$x+y\le 168$

$x\le 0$

$y\le 0$

for $7x+5y\le 1000$

x	5	135
y	193	11

for equation $x+y\le 168$

x	0	168
y	168	0

by graphs

than pain A,B,C

point	lecible solution
A(0,200)	Z=E11,000
B(0,168)	Z=E92,40
C(80,88)	Z=11,240

Finally wheat hector is $80$ and barley hector $88$ than maximum profit is $=11,240$

profit $=E11240$