Economics Homework: Complete Solutions for Tasks 1-12 Analysis

This document presents a comprehensive set of solutions for an economics homework assignment. The solutions cover a range of topics including mathematical calculations, unitary methods, cost analysis, probability, statistical analysis, linear equations, and problem-solving scenarios related to economics. Specifically, the assignment addresses tasks involving calculations with exponents and square roots, applying the unitary method, calculating VAT, determining production costs, calculating probabilities, analyzing data, working with linear equations, solving for variables, and analyzing supply and demand. Furthermore, the assignment also involves applying linear programming to maximize profit, considering production constraints. The document contains detailed step-by-step solutions for each task, demonstrating the application of various economic concepts and mathematical techniques. The solutions are presented in a clear and organized format, providing a thorough understanding of the concepts and calculations involved.

ECONOMICS

TABLE OF CONTENTS
TABLE OF CONTENTS................................................................................................................2
QUESTIONS...................................................................................................................................1
Task 1...........................................................................................................................................1
Task 2...........................................................................................................................................1
Task 3...........................................................................................................................................1
Task 4...........................................................................................................................................2
Task 5...........................................................................................................................................3
Task 6...........................................................................................................................................3
Task 7...........................................................................................................................................4
Task 8...........................................................................................................................................4
Task 9...........................................................................................................................................5
Task 10.........................................................................................................................................6
Task 11.........................................................................................................................................7
Task 12.........................................................................................................................................7

QUESTIONS
Task 1
a) 2.9 – We will first type 2.9 and press multiply button 2 times and then we will press equals
sign for 5 times that gives the answer 594.82
b) 5 √32 – Type 32 and press square root for 5 times that gives the answer as 1.12.
c) 1/(1+0.02)^4 – In this we will press 1 and press divide than type 1.02 and press equal sign for
four times which will give 0.9238 as answer.
d) 500 * 5^-2 – First type 5 and then press multiply two time and then press equal sign it will
give 25 then press subtract sign and then press multiply and type 500 to get -12500 as answer.
e) 23.15+ √50 / (0.9875−3.25) – In this first subtract denominator type 0.9875 and then press
minus button and press equal it will give -2.2625 then press memory (M+). After that type 50
and press square root button which will give 7.072 and press + and type 23.15 which will give
30.22. Press divide button while 30.22 is on screen and press MRC button and press equals
which gives 13.35 as answer.
Task 2
a) Cost of 7 minute call to New York
Applying unitary method
5 minutes = 2.20
7 minutes = ?
= (7 * 2.2) /5
= £3.08
b) Call minutes
Applying unitary method
2.20 = 5 minutes
5.28 = ? minutes
= (5.28 * 5) / 2.2
= 12 minutes
Task 3
a) Time to paint wall by 6 people
4 people = 3 hours
1

1 person takes = 0.75 hours
Extra people time taken = 0.75*2 = 1.5
Total time will reduce by 1.5 hours due to 2 extra people
Therefore time taken by 6 people = 3- 1.5 = 1.5 hours
6 people will take 1.5 hours to paint wall.
b) 12 men = 5 days = 200 m
20 men = ? = 400 m
In 1 day 12 men completes 40 m
In 1 day 20 men will complete = 20 men * 40m /12 men
= 66.66667 m
The days required to complete 400 m = 400m /66.66667
= 6 days
20 men will complete 400 m road in 6 days
c) Super Paint
i) 72 litres in ratio of 7:2
Yellow = 72 *(7/9) = 56
Blue = 72*(2/9) = 16
ii) If 35 litrs of yellow is used
Total paint = 35 *(9*7) = 45
Blue paint = 45 – 35 = 10 litre
Task 4
a)
FV = PV * (1+R)^n
FV = 9500 * (1 + 0.0235)^6
FV = 9500 * 1.1495
FV = £ 10920
b)
2

i) VAT = 90 * 20% = 18
ii) Total cost = 90 + 18 = 108
c) Cost per unit = 6.85 pence = £ 0.00685
Units used = 56.84 / 0.00685
= 817 units
Task 5
Combinations of winning probability
10 groups of 2 items : {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4,
Probability of winning lottery = 1 / (59 :6)
= 6! 53! / 59!
= 6! .
59* 58* 57 *56* 55*54
= 1 / 32441381280
Task 6
Height
x
Weight
y x *y ∑ 𝑥 2
1.65 86 141.9 2.7225
1.43 68 97.24 2.0449
1.56 74 115.44 2.4336
1.74 92 160.08 3.0276
1.55 71 110.05 2.4025
1.67 80 133.6 2.7889
1.58 76 120.08 2.4964
1.47 70 102.9 2.1609
1.51 75 113.25 2.2801
1.61 81 130.41 2.5921
∑ x = 15.77
∑ 𝑦 = 773
∑ 𝑥𝑦 = 1224.95
∑ 𝑥 2 = 24.9495
3

Average height = 1.577
Average weight = 77.3
n x ( ∑𝑥𝑦) - (∑ 𝑥)
x (∑ 𝑦)
10*(1224.95) - (15.77)*(773)
12249.5 - 12190.2
59.3
Task 7
a) Meaning of values 23.12 and 5.34
Equation of line = mx +b
In the given equation 5.34 is the slope of line and 23.12 is y intercept
b)
i) Gradient of line
m = y2- y1 / x2 – x1
= 3- 0 / 0 – 2 =
= 3/2 = 1.5
ii) Equation of line
y = mx + c
y = 1.5 x + 3
iii) Exact value of y
y = 1.5 * 1.5 +3
y = 2.25 + 3
y = 5.25
Task 8
1 meter cotton = 2.5 = a
1 meter silk = 3.5 = b
Total = 6 = c
Sales = 45 metres silk
4

Total sales = £ 780
a) Equation => a = c – b
b) Cotton sales
Total sales = £780
Silk sales = 45 * £3.5 = £157.5
Cotton sales = £780 - £157.5 = £622.5
Cotton sales in metres = 622.5 / 2.5 = 249 metres
c)
1/3 of cotton sold last year = 622.5 / 3 = £207.5
3 times amount of silk sold = £157.5 *3 = £472.5
Total sales of cotton and silk = £472.5 + £207.5 = £680
No the claims of Jill she will only be able to earn £680 following the proposed sales
assumptions.
Task 9
a) 5 + 𝑎 /5 = 12
= (5*5) + a /5 = (12*5)
= 25 + a = 60
= a = 60 – 25
a = 35
b) 3 (5a – 2) = 37.5
= 15a – 6 = 37.5
= 15a = 37.5 – 6
= a = 31.5 / 15
= a = 2.1
c) 4(x + 3) + 6(2x - 1) = 6x + 36
= 4x +12 +12x – 6 = 6x + 36
= 16x + 6 = 6x + 36
= 16x – 6x = 36 – 6
= 10x = 30
5

= x = 30 /10 = 3
d) 𝑎 /5 + 5(𝑎 - 4) = 6 - 2(𝑎 +3)
= a + (5*5)*(a-4) = 5*(6 – 2 (a+3))
= a + 25(a – 4 ) = 30 – 10 (a + 3)
= a + 25 a – 100 = 30 – 10a + 30
= 26a – 100 = 60 – 10a
= 26a + 10a = 100 + 60
= 36a = 160
= a = 160 /36 = 4.44
Task 10
Apples x pence per kg
Oranges y pence per kg
5 kg of apples and 30 kg of oranges cost £41.40
5 kg of apples and 27 kg of oranges cost £37.8
a) Two equations
5x + 30 y = 41.40
5x + 27 y = 37.80
b)
5x + 30 y = 41.40
5x + 27 y = 37.80
0 + 3 y = 3.6
y = 3.6 / 3 = 1.2
5x + 30 y = 41.4
5x + 30*1.2 = 41.4
5x + 36 = 41.4
5x = 41.4 – 36
x = 5.4/5 = 1.08
6

1 kg apple = 1.08
1 kg orange = 1.2
Task 11
a) Relationship between P & Q for supply and demand lines
There is inverse relationship between the demand and supply lines. It could be seen that the price
of the products falls when the supply of products is higher in the market. as per the case if one
unit is purchased it will be costing 300 while if 5 units are purchased it will cost 100 per unit.
From this it could be evaluated that the price of the product falls with the increase in demand.
There is inverse relations means if quantity rises price of the product will fall.
b) It is known as equilibrium point it is the point where the demand and supply are equal.
Task 12
Given
Two types of units are produced
1. Base unit (B)
2. Cabinet unit (C)
Production department Assembly department
Base unit (B) 50 minutes 40 minutes
Cabinet unit (C) 20 minutes 35 minutes
Carpenter each day spends 15 hours 10 hours
Profit contribution
Base Units = £15
Cabinet Units = £32
Solution
Let,
x be number of base units produced in 1 day
y by number of cabinet units produced in 1 day
50x +20y < = 15(60)
7

40x + 35y < = 10(60)
Objective is: maximise ( x+15) + (y+32) = (x + y - 47)
To maximise the profit margins of the units.
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