Chapter 7.5, Problem 91E

To determine

To evaluate: The production level of corporation manufactures.

Answer to Problem 91E

Therefore, the final production levels is $\left[\begin{array}{ccc}\begin{array}{l}84\\ 42\end{array}& \begin{array}{l}60\\ 120\end{array}& \begin{array}{l}48\\ 90\end{array}\end{array}\right]$ .

Explanation of Solution

Given information:

  $\text{A}=\left[\begin{array}{ccc}\begin{array}{l}70\\ 35\end{array}& \begin{array}{l}50\\ 100\end{array}& \begin{array}{l}40\\ 75\end{array}\end{array}\right]$

Calculation: The production levels are increased by 20% so,

  $\begin{array}{l}\text{A}=\left[\begin{array}{ccc}\begin{array}{l}70\\ 35\end{array}& \begin{array}{l}50\\ 100\end{array}& \begin{array}{l}40\\ 75\end{array}\end{array}\right]\\ \text{A}+\left(\frac{20}{100}\right)\text{A}\\ \text{A}+\text{0}\text{.2A}=1.2\text{A}\\ 1.2\text{A}=1.2\times \left[\begin{array}{ccc}\begin{array}{l}70\\ 35\end{array}& \begin{array}{l}50\\ 100\end{array}& \begin{array}{l}40\\ 75\end{array}\end{array}\right]\\ 1.2\text{A}=\left[\begin{array}{ccc}\begin{array}{l}84\\ 42\end{array}& \begin{array}{l}60\\ 120\end{array}& \begin{array}{l}48\\ 90\end{array}\end{array}\right]\end{array}$

Therefore, the final production levels is $\left[\begin{array}{ccc}\begin{array}{l}84\\ 42\end{array}& \begin{array}{l}60\\ 120\end{array}& \begin{array}{l}48\\ 90\end{array}\end{array}\right]$ .