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Linear Programming Problems

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Mr Mattock

on 7 March 2018

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Transcript of Linear Programming Problems

Linear Programming Problems
Starter
Writing constraints
A shop sells two brands of smart phone. The first brand is more popular than the second, so the store always stocks at least twice as many more of the first brand than the second. The shop always keeps both brands in stock. The shop only has shelf space to keep 100 phones altogether. Phones of the first brand are sold for £290, and phones of brand 2 are sold for £350. Work out the number of each brand of phone the shop should stock to maximise profit, and what the maximum profit is.
Writing constraints
The area of a car park is 600 square metres. A car requires 6 square metres, and a bus 30 square metres.
The car park is only allowed to have 60 vehicles altogether. Cars will pay £8 per day, and buses £15 per day. Let x = the number of cars and y = the number of buses. Work out the number of cars and buses that should be allowed in order to maximise income, and what the maximum income is.


L.O. - Use graphical representations of inequalities to solve linear programming problems.
Activity
Complete the linear programming worksheet.
Activities
Activity
Answers

Key
Examples

Worked
Example

Worked
Example

Writing constraints
The area of a car park is 600 square metres. A car requires 6 square metres, and a bus 30 square metres.
The car park is only allowed to have 60 vehicles altogether. Cars will pay £8 per day, and buses £15 per day. Let x = the number of cars and y = the number of buses. Work out the number of cars and buses that should be allowed in order to maximise income, and what the maximum income is.
20 coaches =
20 x 15 = £300.

60 cars =
60 x 8 = £480.

50 cars and 10 coaches = 50 x 8 + 10 x 15 = £550.
Writing constraints
A shop sells two brands of smart phone. The first brand is more popular than the second, so the store always stocks at least twice as many more of the first brand than the second. The shop always keeps both brands in stock. The shop only has shelf space to keep 100 phones altogether. Phones of the first brand are sold for £290, and phones of brand 2 are sold for £350. Work out the number of each brand of phone the shop should stock to maximise profit, and what the maximum profit is.
99 of brand 1 + 1 of brand 2 = £29060

67 of brand 1 + 33 of brand 2 = £30980
Activity
Complete the linear programming worksheet.

1) Belts to Wallets in the ratio 1:2.
2) 88 hours on dump truck and 24 hours on fire engine - Minimum cost = $3480.
3) 9 pounds of food Y and none of food X, giving a minimum cost of $77.33.
4) 270 Traveler Bikes and 30 Tourister bikes, giving maximum of $99000.
A car park charges £8 per day for cars and £15 pound per day for buses.

If the number of cars is x and the number of buses is y, write down and formula for the income, I, that the car park can generate.

Use your formula to work out the income if x = 50 and y = 10.
Starter
A car park charges £8 per day for cars and £15 pound per day for buses.

If the number of cars is x and the number of buses is y, write down and formula for the income, I, that the car park can generate.
I = 8x + 15y

Use your formula to work out the income if x = 50 and y = 10.
I = 8(50) + 15(10) = £550
2
3
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