# linear programming

• Sep 2nd 2009, 07:36 PM
pimpdog847
linear programming
i got to west field high school in Illinois and one of my teacher gave problem that is really confusing. it would be nice if i can get any help.

Here is the problem:

A manufacturer of the garden furniture makes a giverny bench and a kensington bench. The company can produce no more than 60 benches a day. The company needs to produce at least 15 giverny benches and at least 20 kensington benches. The company can produce at most twice as many Kensington benches as Giverny benches. if each giverny sells for \$325 and kensington bench sekks for 250\$. How many of each kind of bench should be produced for maxim profit.

Here are my constrains that i found : X = giverny , Y = Kensington.

X+y<=60
X>=15
Y>=20

i am confuced about this sentence "The company can produce at most twice as many Kensington benches as Giverny benches." what does it mean? is there different constrain for that?
• Sep 3rd 2009, 12:23 AM
Opalg
Quote:

Originally Posted by pimpdog847
i got to west field high school in Illinois and one of my teacher gave problem that is really confusing. it would be nice if i can get any help.

Here is the problem:

A manufacturer of the garden furniture makes a giverny bench and a kensington bench. The company can produce no more than 60 benches a day. The company needs to produce at least 15 giverny benches and at least 20 kensington benches. The company can produce at most twice as many Kensington benches as Giverny benches. if each giverny sells for \$325 and kensington bench sells for 250\$. How many of each kind of bench should be produced for maximum profit.

Here are my constraints that i found : X = giverny , Y = Kensington.

X+y<=60
X>=15
Y>=20

i am confuced about this sentence "The company can produce at most twice as many Kensington benches as Giverny benches." what does it mean? is there different constraint for that? Yes, it tells you that Y <= 2X.

..
• Sep 3rd 2009, 01:10 PM
pimpdog847
what do u mean?(Wondering)
• Sep 3rd 2009, 01:25 PM
Opalg
Quote:

Originally Posted by pimpdog847
what do u mean?(Wondering)

I mean that the sentence "The company can produce at most twice as many Kensington benches as Giverny benches" tells you that Y (the number of Kensingtons) is at most twice x (the number of Givernys). In symbols, $Y\leqslant2X$. That is an additional constraint, to go along with the other ones that you listed.
• Sep 3rd 2009, 08:09 PM
pimpdog847