Let, number of cаnoes bought = x
Number of kayaks bought = y
The optimization function is:
Z=25x+30y
Constraints are:
600∗x+750∗y≤45000
x+y≤65
Since the number of boat can`t be negative,
x≥0,y≥0
The linear programming problem is:
Z=25∗x+30∗y
subject to:
600∗x+750∗y≤45000
x+y≤65
y≥0
x≥0;
Graph:
First equation:
600∗x+750∗y=45000
Divide both parts by 150
4∗x+5∗y=300
Second equation:
x+y=65
Let's solve the system of equations:
{4∗x+5∗y=300x+y≤65
From the first equation we express x:
4∗x+5∗y=3004∗x=300−5∗y(4∗x)/4=(300−5∗y)/4x=75−(5∗y)/4
Substitute the found x into the second equation x+y=65 ;
We get:
y+(75−(5∗y)/4)=6575−y/4=65−y/4=65−75y/4−10y=40
Substitute the found y into the equation:
x=75−(5∗40)/4x=75−50x=25
On solving these we get:
x= number of canoes =25
y= number of kayaks =40
Z =(25×25)+(30×40)=1825
Answer:
Mr. Trenga should buy 25 canoes and 40 kayaks to earn the most revenue.
Maximum revenue is $1825.
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