1. Linear Programming

2. You are in charge of a construction company in Bangkok and you wish to build a hotel with a maximum of 16 rooms. Market research has shown that you should have at least 5 single rooms and at least 8 double rooms. The hotel rooms will cost $60 per single per night and $100 per double per night.
What combination of single and double rooms should be built, so that the nightly revenue is maximised?

3. Let x be the number of single rooms and
y be the number of double rooms.

4. Making the inequalities
at least 5 single rooms
at least 8 double rooms
maximum of 16 rooms

5. Draw the line Draw the line Draw the line Shading unwanted region17 y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x
Draw the line
Draw the line
Draw the line
Double Rooms
Single Rooms

6. Nightly Revenue At (5, 8) At (8, 8) At (5, 11) Double Rooms17 y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x
Single Rooms
Double Rooms
At (5, 8)
At (8, 8)
At (5, 11)

7. You should build a hotel that has 5 single rooms and 11 double rooms.

8. Double Rooms
Single Rooms

11. Chef
You are a chef and you are going to make some fruit cakes and sponge cakes. You have plenty of all the ingredients except for flour and sugar. He has only 2 kg of flour and 1.2 kg of sugar.
A fruit cake uses 500 g of flour and 100 g of sugar.
A sponge cake uses 200 g of flour and 200 g of sugar.
A hotel has made an order for more than 4 cakes.
If you make a profit of 100 Baht on each fruit cake and 90 Baht on each sponge cake find the maximum profit that you can make.

12. Spare time job
You have a spare time job, spraying cars and vans. Vans take 2 hours each and cars take 1 hour each. Bearing in mind all the homework you have to do, you have 14 hours available per week! You have an agreement from Patana School to spray 2 of their vans every week. Apart from that you have no fixed work.
As you do the work in your back garden the local authorities have made a condition that you must do at least twice as many cars as vans.
If you make a profit of 1000 Baht for each car and 2500 Baht for each van, find the maximum profit you can make.

13. Football Manager
You are a manager of a local football team and you have $96 to spend on buying on new players. You can buy defenders at $6 each and forwards at $8 each. You need at least 6 of each sort. To cover for injuries you must buy at least 13 players altogether. If the wages are $10 per week for each defender and $20 per week for each forward, what is the combination of players, which will give you the lowest wage bill.

14. Tennis-playing golfer
You are a tennis playing golfer and have 1500 Baht to spend on golf balls costing 150 Baht each and tennis balls costing 100 Baht each. You need to buy at least 10 altogether and you decide that you need more golf balls than tennis balls. After using them you sell the golf balls for 20 Baht each and tennis balls for 30 Baht each. What is the maximum possible income from the sales?