1.A firm produces 4 kinds of goods: G1, G2, G3, G4. Each good requires three kin
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Question
1.A firm produces 4 kinds of goods: G1, G2, G3, G4. Each good requires three kinds of input: Labor, Row Materials, Capital (quantity if each input needed for each good is noted in the table below) There are 14 units of Labor, 15 units of row materials, and 10 units of capital. Find quantity of each good if all inputs are utilized in these goods production.
2.A construction firm is going to build 6 residential, 3 commercial, and 4 industrial buildings. It needs bricks, cement, wood, metal, and glass, the prices of which are 32$, 300$, 44$, 6$, and 5$ per unit respectively. The table below summarized amounts of material of each kind required for each type of building:
Find:
(a) Total quantity of each type of material;
(b) Cost of building each type of building;
(c) Total cost of construction
G1 G2 G3 G4 L 3 2 2 1 RM 2 5 2 3 C 1 2 2 3Explanation / Answer
Answer 1
For finding the quantity of each good we will divide the data in below ratio:
For calculating value of column labour we will multiply each data of above chart by 14 and divide the obtained result by 8(Total of labour in above chart).For example in case of G1 (3*14/8= 5.25)
For calculating value of column Raw material we will multiply each data of above chart by 15 and divide the obtained result by 12(Total of Raw material in above chart).For example in case of G1 (2*15/12= 2.5)
For calculating value of column capital we will multiply each data of above chart by 10 and divide the obtained result by 8(Total of capital in above chart).For example in case of G1 (1*10/8= 1.25)
Total Input
G1
G2
G3
G4
Labour
14
5.25
3.5
3.5
1.25
Raw material
15
2.5
6.25
2.5
3.45
Capital
10
1.25
2.5
2.5
3.25
Total Output
9
12.25
8.5
9.25
Answer 2
( a) Total quantity of Bricks required in construction of 6 residential, 3 commercial, and 4 industrial buildings=78*6+84*3+60*4 = 960
Total quantity of cement required in construction of 6 residential, 3 commercial, and 4 industrial buildings = 9*6+10*3+8*4 = 116
Total quantity of wood required in construction of 6 residential, 3 commercial, and 4 industrial buildings = 41*6+40*3+35*4 = 506
Total quantity of metal required in construction of 6 residential, 3 commercial, and 4 industrial buildings = 210*6+200*3+180*4 = 2580
Total quantity of glass required in construction of 6 residential, 3 commercial, and 4 industrial buildings = 120*6+140*3+160*4 = 1780
(b) Cost of building one residential building = 78*32+9*300+41*44+210*6+120*5 =$8860
Cost of building one commercial building = 84*32+10*300+40*44+200*6+140*5 = $9348
Cost of building one industrial building = 60*32+8*300+35*44+180*6+160*5 = $7740
(c) Total cost of constructing 6 residential, 3 commercial, and 4 industrial buildings =
6*8860+3*9348+4*7740 = $112164
Total Input
G1
G2
G3
G4
Labour
14
5.25
3.5
3.5
1.25
Raw material
15
2.5
6.25
2.5
3.45
Capital
10
1.25
2.5
2.5
3.25
Total Output
9
12.25
8.5
9.25
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