Chapter 3.2, Problem 56E

Accounting Consider the original budget matrix in Problem $55$. Assume that there is a $20\%$ increase in manufacturing, a 3% increase in office, a 5% increase in sales, a 20% increase in shipping, a 5% increase in accounting, and a 3% decrease in management. Find the new budget matrix by developing a matrix $A$ to represent these departmental increases and then multiply it from the left by the matrix $B$ in Problem 55.

Accounting The annual budget of the Magnum Company has the following expenses, in thousands of dollars, for selected departments.

$\begin{array}{l}\begin{array}{lllllll}\hfill & Mfg.\hfill & Office\hfill & Sales\hfill & Shp.\hfill & Act.\hfill & Mgt.\hfill \\ Supplies\hfill & 0.7\hfill & 8.5\hfill & 10.2\hfill & 1.1\hfill & 5.6\hfill & 3.6\hfill \\ Phone\hfill & 0.5\hfill & 0.2\hfill & 6.1\hfill & 1.3\hfill & 0.2\hfill & 1.0\hfill \\ Transp.\hfill & 2.2\hfill & 0.4\hfill & 8.8\hfill & 1.2\hfill & 1.2\hfill & 4.8\hfill \\ Salaries\hfill & 251.8\hfill & 63.4\hfill & 81.6\hfill & 35.2\hfill & 54.3\hfill & 144.2\hfill \\ Utilities.\hfill & 30.0\hfill & 1.0\hfill & 1.0\hfill & 1.0\hfill & 1.0\hfill & 1.0\hfill \\ Materials\hfill & 788.9\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \end{array}\\ \begin{array}{l}Mfg.=Manufacturing;Shp.=Shipping;\hfill \\ Act.=Accounting;Mgt.=Management\hfill \end{array}\end{array}$

Write a matrix $B$ for these budget amounts.

Write the matrix $A$ so that $BA$ would contains new budget figures that reflect an $11\%$ increase in manufacturing, sales, and shipping, and a $5\%$ decrease in the other departments.