Answer to Question #191556 in Math for EUGINE HAWEZA

Question

The following information gives the numbers of journeys made by the delivery department of a small company: From: A B с D To A 0 3 4 2 B 1 0 0 6 С 1 2 0 2 D 4 3 0 0 The company has four different depots and the above table indicates that there was one journey made from depot A to Depot B and three journeys made from B to A and so on and so forth. .

This second table gives the loading costs per load for goods leaving each depots. Depot Cost (in 000) A k120 B k105 C k110 D k100 It costs k130000 to load for trip at Depot A. K115000 at Depot B and so on and so forth

a) i) Write these two sets of information as matrices

ii. Find the product of the two matrices

b) Explain the meaning of the entries in the product matrix

Answer 1

(i) Matrix of the no. of journeys from one dept. to another

   $P= \begin{bmatrix} 0&3&4&2\\1&0&0&6\\1&2&0&2\\4&3&0&0\end{bmatrix}$

 Cost matrix can be written as a column matrix as-

  $X=\begin{bmatrix} k120\\k105\\k110\\100\end{bmatrix}$

 (ii) Product 

     $PX= \begin{bmatrix} 0&3&4&2\\1&0&0&6\\1&2&0&2\\4&3&0&0\end{bmatrix}\begin{bmatrix} k120\\k105\\k110\\100\end{bmatrix}$

        $=\begin{bmatrix}k955\\k720\\k530\\k795 \end{bmatrix}$

(iii) This PX matrix shows that the total cost of total delivery get b any depot.

      For Ex- Depot 'A' get K955 delivery from other three dept. Similarly , Depot 'B' get K720cost of delivery by other three department A,C,D. and so on.