Question

Formulate the situation in matrix form. Be sure to indicate the meaning of your rows and columns. Find the requested quantities using the appropriate matrix arithmetic. A sports apparel company manufactures shorts, tee shirts, and caps in Costa Rica and Honduras for importation and sale in the United States. In Costa Rica the labor costs per item are 60¢ per pair of shorts, 30¢ per tee shirt, and 45¢ per cap, while the costs of the necessary materials are $1.60 per pair of shorts, 85¢ per tee shirt, and $1.15 per cap. In Honduras the labor costs per item are 90¢ per pair of shorts, 20¢ per tee shirt, and 50¢ per cap, while the costs of the necessary materials are $1.50 per pair of shorts, 80¢ per tee shirt, and $1.10 per cap. Represent these costs as a labor cost matrix L and a materials cost matrix M. Use these matrices to find the total cost matrix C for these products in these countries. (Let the first row represent the cost, in pennies, in Costa Rica and the second row represent the cost, in pennies, in Honduras.)

Answer 1

Answer: and Step-by-step explanation: The matrix L is of form 2x3, in which therentwo rows, representing Costa Rica and Honduras, respectively, and 3 columns, representing pair of shorts, tee shirt and cap, respectively:

L = $\left[\begin{array}{ccc}0.6&0.3&0.45\\0.9&0.2&0.5\end{array}\right]$

The matrix M is also a matrix of form 2x3:

M = $\left[\begin{array}{ccc}1.6&0.85&1.15\\1.5&0.8&1.1\end{array}\right]$

Matrix C is the total cost of both countries, then:

C = L + M

C = $\left[\begin{array}{ccc}0.6&0.3&0.45\\0.9&0.2&0.5\end{array}\right]$ + $\left[\begin{array}{ccc}1.6&0.85&1.15\\1.5&0.8&1.1\end{array}\right]$

To add 2 matrices, you have to add the first term of the first matrix to the first term of the second matrix and so on:

C = $\left[\begin{array}{ccc}0.6+1.6&0.3+0.85&0.45+1.15\\0.9+1.5&0.2+0.8&0.5+1.1\end{array}\right]$

C = $\left[\begin{array}{ccc}1.6&1.15&1.6\\2.4&1&1.6\end{array}\right]$

The total cost for the products in each country is

C = $\left[\begin{array}{ccc}1.6&1.15&1.6\\2.4&1&1.6\end{array}\right]$