### Using and Managing Data and Information

### BA3020QA – Assignment 1

__Task 1: ( 10 marks)__

- 8 people can paint a fence in 3 hours. How long will it take 12 people to paint the same fence (Assume everyone works at the same rate). You must show all your workings.
- A tyre dealer sells 510 standard tyres in July generating revenue of £25,500. How much revenue is generated the following month, with the same unit price if 670 tyres are sold? You must show all your workings.
- 12 men take 5 days to build a road 200m long. How many days will 20 men take to build a similar road which is 400m long? Explain your answer in details.
- Super Paint is mixed by using yellow and blue in the ratio 7:2
- How much yellow and how much blue must be used to make 72 litres of the super paint?
- How much blue is used if 35 litres of yellow is used?

__Task 2: ( 10 marks)__

- How many combinations of 4 students can be made from a class of 30 students? Show all your workings.
- How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9 inclusive? Show all your workings.
- You consider entering a Lottery, where you choose six different numbers between 1 to 50 inclusive. Explain in words how you would calculate the possible combinations of winning the jackpot (i.e., obtaining all six numbers).

Show all the steps in your calculation. (You should not use the formula in the calculator)

__Task 3: ( 10 marks)__

For this task, you need to show all your calculations, step by step.

- Steven receives an electricity bill for £90. The bill includes a quarterly charge of £15 and the cost per unit is 6 pence. Calculate to the nearest whole number, the quantity of units he has used.
- A first-time house buyer can make 360 monthly payments of £480 to repay the mortgage. How many monthly payments are required if he can pay £450 per month?
- A second-hand car dealer was offering a 20% discount for a car, with a sales price £6,400 for immediate cash sales. What was the original price before the discount?

__Task 4: ( 10 marks)__

- The equation of a line is given as
How is the value 5 calculated?*y = 5x + 8* - In the diagram below:
- Find the gradient of the line
- Write the equation of the line in the form
*y = mx + b* - Find the exact value of
*y*when*x*is 6

Explain your methods clearly

__Task 5: ( 10 marks)__

In this task, you are asked to formulate the linear programming problem below and then solve it.

A sub-contractor produces two types of units for a kitchen manufacturer, a base unit (B) and cabinet unit (C).

The **base unit** requires 15 minutes in the production department and 40 minutes in the assembly department.

The **cabinet unit** requires 20 minutes in the production department and 30 minutes in the assembly department.

The production and assembly of these two units are done by specialist carpenters who are in short supply. Each day only 5 hours in the production department are available and only 10 hours are available in the assembly department.

Once sold, the base units contribute £5 to profit and the cabinet units £3 to profit.

*Required:*

Formulate the Linear Programming problem above by defining the control variables, stating the object function and the constraints.

You are required to produce the graph for all inequalities and clearly show the feasible region. (copy image to Word)

Find the quantity of units to maximise profit.

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