# Linear Programming

• Feb 19th 2008, 01:47 AM
benjiman
Linear Programming
An outdoor clothing manufacturer has 520 metres of polarfleece material. the manufacturer will use it to make jackets of two types, Polarbear and Polarfox, to sell to retailers. For each jacket of either type, 2.0 metres of material is required. However, the Polarbear is simpler in design, requiring 2.4 hours each in the production process while each Polarfox requires 3.2 hours. There are 672 hours available.
From past experience of demand, the manufacturer has decided to make no more than half as many Polarfox jackets as Polarbear jackets. If the profit on each Polarbear jacket is \$36 and the profit on each Polarfox jacket is \$42, use a graphical method to find how many of each type should be made in order to maximise profit. What is the maximum profit?

Well first of all, i tried to work out the constraints....
x>- 2, y>- 2
2.4x+3.2y-< 672
y-< 1/2x
P=36x+42y

All of the three graphs do not intersect at the same point and therefore i'm not able to find x and y..........
• Feb 19th 2008, 02:09 AM
CaptainBlack
Quote:

Originally Posted by benjiman
An outdoor clothing manufacturer has 520 metres of polarfleece material. the manufacturer will use it to make jackets of two types, Polarbear and Polarfox, to sell to retailers. For each jacket of either type, 2.0 metres of material is required. However, the Polarbear is simpler in design, requiring 2.4 hours each in the production process while each Polarfox requires 3.2 hours. There are 672 hours available.
From past experience of demand, the manufacturer has decided to make no more than half as many Polarfox jackets as Polarbear jackets. If the profit on each Polarbear jacket is \$36 and the profit on each Polarfox jacket is \$42, use a graphical method to find how many of each type should be made in order to maximise profit. What is the maximum profit?

Well first of all, i tried to work out the constraints....
x>- 2, y>- 2
2.4x+3.2y-< 672
y-< 1/2x
P=36x+42y

All of the three graphs do not intersect at the same point and therefore i'm not able to find x and y..........

Let b be the number of Polarbear jackets manufactured, and f be the number
of Polarfox jackets manufactured.

Time constraint:

2.4b+3.2f <= 672

Material constraint:

2b+2f<= 520

Experience constaint:

f-2b<=0

Implicit constaints:

f>=0, b>=0.

Objective:

O=36b+42f

RonL
• Feb 19th 2008, 02:36 AM
benjiman
The intersection points of these are (168,84)
which gives P=168*36+84*42=9576.

The actual answer is (200, 60)
Where the maximum profit is \$9720.

Can you fix it and work back there again...
• Feb 19th 2008, 07:06 AM
CaptainBlack
Quote:

Originally Posted by benjiman
The intersection points of these are (168,84)
which gives P=168*36+84*42=9576.

The actual answer is (200, 60)
Where the maximum profit is \$9720.

Can you fix it and work back there again...

Have you checked all the vertices of the feasible region?

Then check the other vertices.

RonL