ECONOMICS

Economics

Economics

A firm called Sleek Ltd. makes wooden tables: they wish to choose the most profitable combination of labour and machinery. They pay £ 8 per hour to each employee they hire. They also hire woodworking machines, which cost £ 3 per hour to hire. Each member of staff makes tables (there are no other staff, such as managers or security staff). The number of machines used must be a whole number.

Answer: Part (A)

The graph for the combinations of affordable person-machine hours to be employed is generated based on the following tabulated information:

Combinations

A

B

C

D

E

F

G

H

I

J

Person-hours

7.5

7.12

6.75

6.37

6

5.62

5.25

4.87

4.5

4.12

Machine-hours

0

1

2

3

4

5

6

7

8

9

Combinations

K

L

M

N

O

P

Q

R

S

T

U

Person-hours

3.75

3.37

3

2.62

2.25

1.87

1.5

1.12

0.75

0.37

0

Machine-hours

10

11

12

13

14

15

16

17

18

19

20

The graph is represented on the next page, where the x-axis represents the machine-hours and the y-axis represents the person-hours. The display of the graph is more like a production possibility curve (PPC), also known as the production possibility frontier (PPF).

The graph does not suggest the most efficient combination for Sleek Ltd. to select from. In fact, it does not represent anything worth decision making except for the different combinations of person-hours and machine-hours that can be used staying within the budget of £60.

Answer: Part (B)

The output of Sleek Ltd. is given by the production function N = 7 K0.3 L0.2 where N is the number of tables made per hour, K is the number of machines used, and L the number of employees. The graph that displays the combinations of employees and machines, which can produce 18.4 tables per hour with machines ranging from 5 to 20, is generated based on the following tabulated information:

Combinations

A

B

C

D

E

F

G

H

Person-hours

11.2

8.54

6.77

5.55

4.65

3.97

3.44

3.02

Machine-hours

5

6

7

8

9

10

11

12

Total Cost

105

86.3

75.21

68.4

64.18

61.7

60.52

60.1

Tables Produced

18.4

18.4

18.4

18.4

18.4

18.4

18.4

18.4

Combinations

I

J

K

L

M

N

O

P

Person-hours

2.67

2.4

2.16

1.96

1.79

1.64

1.52

1.4

Machine-hours

13

14

15

16

17

18

19

20

Total Cost

60.42

61.2

62.28

63.7

65.32

67.1

69.12

71.2

Tables Produced

18.4

18.4

18.4

18.4

18.4

18.4

18.4

18.4

The graph is represented on the next page, where the x-axis represents number of machines used in the combination for producing 18.4 tables per hour. The machines start from '5', which is why the x-axis does not start from '1'. The y-axis denotes the number of employee-hours used.

The above graph shows that as the use of number of machines increases the number of employee's hour's decreases. Similarly, the more hours of the employees are hired, the less number of the machine hours will be used. This is because there is an indirectly proportional relationship between the two variables.Answer: Part (C)

The labour cost of producing 18.4 tables per hour if Sleek Ltd. employed 5 machines can be calculated based on the following calculations:

1 Machine cost per hour = £ 3

1 Employee labour cost per hour=£ 8

Employee hours utilized (From Part B) =11.2

Machines utilized=5

Total Cost = (Machine cost/hr x Machine utilized) + (Labour cost/hr x Employee hours utilized)

Total Cost = (3 x 5) + (8 x 11.2)

Total Cost = (15) + (89.6)

Total Cost = £ 104.6

The total cost of manufacturing wooden tables including the labour and machinery, in the first combination of resources based on part (B) is £ 104.6.

Answer: Part (D)

The labour cost of producing 18.4 tables per hour if Sleek Ltd. employed 6 machines can be calculated based on the following calculations:

1 Machine cost per hour = £ 3

1 Employee labour cost per hour=£ 8

Employee hours utilized (From Part B) =8.54

Machines utilized=6

Total Cost = (Machine cost/hr x Machine utilized) + (Labour ...