VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: einsteinreborn on July 20, 2013, 09:03:20 pm
Title: Linear Programming question
Post by: einsteinreborn on July 20, 2013, 09:03:20 pm
Hi guys
just wanted some help with this question. I've got the constraints down, but when I draw the graph I'm finding it hard to find the feasible region. Any help is appreciated. The question is:
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?
I know the constraints must be :
2x+2y<=520 2.4x+3.2y<=672 y<=1/2x
though I'm finding it hard to find the feasible region and my points of intersection don't fit in the constraints.
Title: Re: Linear Programming question
Post by: scribble on July 20, 2013, 09:55:27 pm
all your conditions are correct. (and you also need x>=0 and y>=0) so if you graph it(on your calculator), the points of intersection that fit the constraints are (200,60) , (168, 84). theyre pretty big numbers so you need to zoom riight out to get the points. (173,86) is another point of intersectin, but it doesn't fit the constraint 2.4x+3.2y<=672, so you don't use it.
when your profit is 36x+42y is you sub (200, 60) in you get P=9720 and if you sub (168, 84) in you get P=9576
so the maximum profit is $9720 :)
Title: Re: Linear Programming question
Post by: RKTR on July 20, 2013, 09:57:05 pm
yea i get 168 and 84 too
Title: Re: Linear Programming question
Post by: b^3 on July 20, 2013, 10:00:47 pm
This might help you too, the required region is the white, non-shaded region below.
Title: Re: Linear Programming question
Post by: einsteinreborn on July 20, 2013, 10:29:15 pm
Thanks a lot guys. The graph sketch really put it into perspective for me. I was confused about that point that didn't fit the constraints but now it all makes sense.