Chapter 7.5, Problem 87E

a)

To determine

To find:the profit per unit matrix.

Answer to Problem 87E

  $B=\left[\begin{array}{cc}\$3.50& \$6.00\end{array}\right]$

Explanation of Solution

Given information:

A farmer grows apples and peaches.Each crop is shipped to three different outlets. Theshipment levels are represented by $A$ .

  

Grower earns $3.50 profits per unit of apples and $6.00 profits per unit peaches.

Calculations:

Grower earns $3.50 profits per unit of apples and $6.00 profits per unit peaches.

If the profit is arranged in a matrix it will be of dimension $1\times 2$ .

The profit per unit can be represented by the matrix $B=\left[\begin{array}{cc}\$3.50& \$6.00\end{array}\right]$

b)

To determine

To find: $BA$ and interpret the result.

Answer to Problem 87E

  $BA=\left[\begin{array}{ccc}1037.5& 1400& 1012.5\end{array}\right]$ .

The entries represent the profits from both crops at each of three outlets.

Explanation of Solution

Given information:

A farmer grows apples and peaches.Each crop is shipped to three different outlets. Theshipment levels are represented by $A$ .

  

The profit per unit are represented by the matrix $B=\left[\begin{array}{cc}\$3.50& \$6.00\end{array}\right]$ .

Concept used:

The product of matrix A and B exist only if the number of columns in matrix A is equal to the number of rows in matrix B .

Calculations:

Now, calculate the product BA as shown:

  $\begin{array}{l}BA=\left[\begin{array}{cc}3.50& 6.00\end{array}\right]\left[\begin{array}{ccc}125& 100& 75\\ 100& 175& 125\end{array}\right]\\ =\left[\begin{array}{ccc}3.50\times 125+6.00\times 100& 3.50\times 100+6.00\times 175& 3.50\times 75+6.00\times 125\end{array}\right]\\ =\left[\begin{array}{ccc}1037.5& 1400& 1012.5\end{array}\right]\end{array}$

Conclusion:

Thus, the entries represent the profits from both crops at each of three outlets.