Chapter 7.5, Problem 112E

a.

To determine

To find: the value of $a_{21}$ .

Answer to Problem 112E

The value of $a_{21}$ is $6000$ .

Explanation of Solution

Given information :

  $A=\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]$

Calculation : since,

  $A=\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]$ ,

Form the above matrix it can be observed that $a_{21}=6000$ .

b.

To determine

To find: the shipment level when the shipment are increased by $15\%$ .

Answer to Problem 112E

The shipment level when the shipment are increased by $15\%$ is $\left[\begin{array}{l}\text{750 600 1200 }\\ \text{900 1500 750 }\end{array}\right]$ .

Explanation of Solution

Given information :

  $A=\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]$

Calculation to find the production level when production is increased by $15\%$ , multiply the production level by $15\%$ ,

  $\begin{array}{l}15\%A=15\%\text{ of}\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]\\ 15\%A=\frac{15}{100}\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]\\ 15\%A=\left[\begin{array}{l}\text{750 600 1200 }\\ \text{900 1500 750 }\end{array}\right]\text{ [simplify]}\end{array}$

c.

To determine

To state: that by using matrices the cost of LCD televisions at each ware house can be found.

Answer to Problem 112E

To find the cost of the two models of LCD televisions at each warehouse, consider the matrices columns because the columns represents the warehouse.

Explanation of Solution

Given information :

  $A=\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]$

since,

  $A=\left[\begin{array}{l}\text{5000 4000 8000}\\ \text{6000 10000 5000}\end{array}\right]$ ,

To find the cost of the two models of LCD televisions at each warehouse, consider the matrices columns because the columns represents the warehouse.