Reference no: EM133083184
BA3020QA Using and Managing Data and Information
Assessment Task 1:
The data in the table below shows the height of athletes in metres and their respective weights in kilograms.
|
Height (x)
|
1.65
|
1.43
|
1.56
|
1.74
|
1.50
|
1.67
|
1.58
|
1.47
|
1.51
|
1.60
|
|
Weight (y)
|
86
|
68
|
74
|
92
|
71
|
80
|
76
|
70
|
75
|
81
|
Explain how you would calculate the following. Show all your workings.
a. ∑x=
b. ∑y=
c. ∑xy=
d. ∑x2=
e. Calculate the average height
f. Calculate the average weight
g. Showing all the steps, calculate:
n x ( ∑xy) - (∑x) x (∑y)
Task 2:
a. How many combinations of 3 students can be made from a class of 15 students? Show all your workings.
b. You consider entering a Lottery, where you choose 5 different numbers between 1 to 40 inclusive. Explain in words how you would calculate the possible combinations of winning the jackpot (i.e., obtaining all five numbers).
Show all the steps in your calculation. (You should not use the formula in the calculator)
Task 3:
For this task, you need to show all your calculations, step by step.
a. Mr Frank receives an electricity bill for £60. The bill includes a quarterly charge of £10 and the cost per unit is 5 pence. Calculate to the nearest whole number, the quantity of units he has used.
b. A first-time house buyer can make 360 monthly payments of £680 to repay the mortgage. How many monthly payments are required if he can pay £650 per month?
c. A second-hand car dealer was offering a 25% discount for a car, with a sales price £1,900 for immediate cash sales. What was the original price before the discount?
Task 4:
a) The equation of a line is given as y = 3x + 6
How is the value 3 calculated?
b. In the diagram below:
c. Find the gradient of the line
d. Write the equation of the line in the form y = mx + b
e. Find the exact value of y when x is -1
Explain your methods clearly.
Task 5:
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 40 minutes in the production department and 50 minutes in the assembly department.
The cabinet unit requires 30 minutes in the production department and 20 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 14 hours in the production department are available and only 8 hours are available in the assembly department.
Once sold, the base units contribute £30 to profit and the cabinet units £40 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.
Attachment:- Using and Managing Data and Information.rar