You are Here: Home >< Maths

# D1 Linear Programming exam question from January 2013 paper Watch

1. Hi,

Can someone help me with this linear programming question please?

A factory can make three different kinds of balloon pack: gold, silver and bronze.
Each pack contains three different types of balloon: type A, B & C.

• Each gold pack has 2 type A balloons, 3 type B balloons and 6 type C balloons.
• Each silver pack has 3 type A balloons, 4 type B balloons and 2 type C balloons.
• Each bronze pack has 5 type A balloons, 3 type B balloons and 2 type C balloons.

Every hour, the maximum number of each type of balloon available is 400 type A, 400 type B and 400 type C.

Every hour, the factory must pack at least 1000 balloons.

Every hour, the factory must pack more type A balloons than type B balloons.

Every hour, the factory must ensure that no more than 40% of the total balloons packed are type C balloons.

Every hour, the factory makes x gold, y silver and z bronze packs.

Formulate the above situation as 6 inequalities, in addition to x≧0, y≧0, z≧0, simplifying your answers.

Thank you anyone who answers
2. A factory can make three different kinds of balloon pack: gold, silver and bronze.
Each pack contains three different types of balloon: type A, B & C.

• Each gold pack has 2 type A balloons, 3 type B balloons and 6 type C balloons.
• Each silver pack has 3 type A balloons, 4 type B balloons and 2 type C balloons.
• Each bronze pack has 5 type A balloons, 3 type B balloons and 2 type C balloons.

Every hour, the maximum number of each type of balloon available is 400 type A, 400 type B and 400 type C.

Every hour, the factory must pack at least 1000 balloons.

Every hour, the factory must pack more type A balloons than type B balloons.

Every hour, the factory must ensure that no more than 40% of the total balloons packed are type C balloons.

Every hour, the factory makes x gold, y silver and z bronze packs.

Formulate the above situation as 6 inequalities, in addition to x≧0, y≧0, z≧0, simplifying your answers.
3. (Original post by Shel-Bot)
Hi,

Can someone help me with this linear programming question please?

A factory can make three different kinds of balloon pack: gold, silver and bronze.
Each pack contains three different types of balloon: type A, B & C.

• Each gold pack has 2 type A balloons, 3 type B balloons and 6 type C balloons.
• Each silver pack has 3 type A balloons, 4 type B balloons and 2 type C balloons.
• Each bronze pack has 5 type A balloons, 3 type B balloons and 2 type C balloons.

Every hour, the maximum number of each type of balloon available is 400 type A, 400 type B and 400 type C.
2x+3y+5z<=400
3x+4y+3z<=400
6x+2y+2z<=400
Every hour, the factory must pack at least 1000 balloons.
30x+30y+30z>=1000
Every hour, the factory must pack more type A balloons than type B balloons.
2x+3y+5z>3x+4y+2z (simplify)
Every hour, the factory must ensure that no more than 40% of the total balloons packed are type C balloons.
6x+2y+2z<=12x+12y+12z (0.4*30=12)
Every hour, the factory makes x gold, y silver and z bronze packs.
4. What working out have you done so far? Your starting basis can be to make an algebraic equation for each packet.
E.g. 1 Gold = 2A + 3B + 6C
5. Thank you!

This really helps me!
6. (Original post by ztibor)
30x+30y+30z>=1000
Don't think that part is correct.
7. (Original post by ghostwalker)
Don't think that part is correct.
Ok. Thank's.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 4, 2013
Today on TSR

### Is this person a genius?

...with these A Level results?

### I think I'm transgender AMA

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.