Chapter 4.6, Problem 60SR

(a)

To determine

To Find: The inventory matrix for the number of the cases for each type of fruit for each farm and the cost of matrix for the price per case for each type of fruit.

Answer to Problem 60SR

The inventory matrix is $I=\left[\begin{array}{ccc}290& 165& 210\\ 175& 240& 190\\ 110& 75& 0\end{array}\right]$ and the cost matrix is $C=\left[\begin{array}{c}22\\ 25\\ 18\end{array}\right]$ .

Explanation of Solution

Given:

The given Table for the number of cases in stock of each type of fruit is shown in Table 1

Table 1

Fruit	Farm 1	Farm 2	Farm 3
Apples	292	175	110
Peaches	165	240	75
Apricots	210	190	0

The selling price of apple is $22, peaches is $25 and apricots is $18.

Calculation:

The inventory matrix for the number of cases of each type of fruit for each farm is,

  $I=\left[\begin{array}{ccc}290& 165& 210\\ 175& 240& 190\\ 110& 75& 0\end{array}\right]$

Then, the cost matrix is,

  $C=\left[\begin{array}{c}22\\ 25\\ 18\end{array}\right]$

Thus, the inventory matrix is $I=\left[\begin{array}{ccc}290& 165& 210\\ 175& 240& 190\\ 110& 75& 0\end{array}\right]$ and the cost matrix is $C=\left[\begin{array}{c}22\\ 25\\ 18\end{array}\right]$ .

(b)

To determine

To Find: The total income of the three fruits farms expressed as the matrix.

Answer to Problem 60SR

The income for the total matrix is $\left[\begin{array}{c}14285\\ 13720\\ 18\end{array}\right]$ .

Explanation of Solution

Consider the total income of the three fruit farm is obtained as,

  $\begin{array}{c}\left[\begin{array}{ccc}290& 165& 210\\ 175& 240& 190\\ 110& 75& 0\end{array}\right]\left[\begin{array}{c}22\\ 25\\ 18\end{array}\right]=\left[\begin{array}{ccc}290\left(22\right)& 165\left(25\right)& 210\left(18\right)\\ 175\left(22\right)& 240\left(25\right)& 190\left(18\right)\\ 110\left(22\right)& 75\left(25\right)& 0\left(18\right)\end{array}\right]\\ =\left[\begin{array}{c}14285\\ 13720\\ 18\end{array}\right]\end{array}$

(c)

To determine

To Find: The total income for all the three fruit jams.

Answer to Problem 60SR

Thus, the total income is $\$31850$ .

Explanation of Solution

The total income for the fruit jam is obtained as,

  $14285+13270+4295=\$31850$