Product P uses 3 units of material, 9 units of labour and 12 units of capital;
product Q uses 6, 9 and 15 units respectively and product R uses 9, 2 and 9
units of these respectively. A total of 80 units of material, 60 units of labour and
125 units of capital are available. Find how many units of the three products
could be produced by making use of available material, labour and capital with the help of matrix algebra.
Answers
Answer:
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Answer:
Material = 80/135
Labor = 60/135
Capital = 125/135
Step-by-step explanation:
Given:
Three products P,Q,R are using units in the order,
P - 3 units of material, 9 units of labor, 12 units of capital
Q - 6 units of material, 9 units of labor, 15 units of capital
R - 9 units of material, 2 units of labor, 9 units of capital
A total of 80 units of material, 60 units of labor, 125 units of capital
To find:
How many units of the three products could be produced by making use of available material, labor, capital
Solution:
Matrix = , A =
=
= 3[(9*9)-(15*2)]-9[(6*9)-(15*9)]+12[(6*2)-(9*9)]
⇒ 3[(81)-(30)]-9[(45)-(135)]+12[(12)-(81)]
⇒ 3(51)-9(-90)+12(-69)
⇒ 3(51)+810-828
⇒ 153+810-828
⇒ 135
Hence,
Material = 80/135
Labor = 60/135
Capital = 125/135
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