Question

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.

Answer 1

Answer:

this is good question ok

Answer 2

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 = $\left[\begin{array}{ccc}3&9&12\\6&9&15\\9&2&9\end{array}\right]$, A = $\left[\begin{array}{ccc}80\\60\\125\end{array}\right]$

$\left[\begin{array}{ccc}80\\60\\125\end{array}\right]$ = $\left[\begin{array}{ccc}3&9&12\\6&9&15\\9&2&9\end{array}\right]$

$\left[\begin{array}{ccc}80\\60\\125\end{array}\right]$ = 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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