Chapter 8.2, Problem 86E

(a)

To determine

To interpret: the value of $a_{22}$ .

Answer to Problem 86E

  $a_{22}$ interprets the number of electric guitars manufactured by the company $B$ .

Explanation of Solution

Given information:

A corporation has three factories that manufacture acoustic guitans and electric guitans. The production levels are represented by $A$ .

Calculation:

The production levels are represented by

  $A=\left[\begin{array}{ccc}70& 50& 25\\ 35& 100& 70\end{array}\right]$

Here value of $a_{22}=100$ (the second row second element)

It interprets the number of electric guitars manufactured by the company $B$

(b)

To determine

To find: the use of matrices to calculate the production levels when production increases by 20%.

Answer to Problem 86E

  $A$ is multiplied by 1.20.

Explanation of Solution

If the production level is increased to 20% then add $0.20A$ to the matrix $A$

Then $A+0.20A=\left(1.2\right)A$

It means each element of matrix $A$ is multiplied by 1.20.

(c)

To determine

To find: the use of the matrices to calculate the total sales value of the guitars produced at each factory.

Answer to Problem 86E

Total sales of guitars at each factory is calculated by evaluating $BA$ .

Explanation of Solution

Given information:

Each acoustic guitar sells for $80 and each electric guitar sells for $120.

Calculation:

Acoustic guitar sells $80, electric guitar sells for $120

Here selling price is represented by the matrix $B=\left[80120\right]$

Now total sales of guitars at each factory is calculated by evaluating $BA$ .