Questan Help wo departments of a frm, A and B, need differing amounts of steel,

Question

Questan Help wo departments of a frm, A and B, need differing amounts of steel, wood, and plastic. The table on the right gives the amount of each product the departments need Steel TO 50 40 40 50 artment E These three products are supplied by two suppliers, Company C and Company D, with the unit prices given in the table on the right. Steel Wood290 610 200 410 a. Use matrix multiplicaton to determine how much these orders will cost each department at each of the two supplers. Enter the amounts into the cos matrix shown on the right. Co C Co. D Dept A Dept B L D b. From which supplier should each department make its purchase? Which compary should department A use? O Company C O Company D Which company should department B use O Company D O Company C

Explanation / Answer

Solution:

We are given two Dept A and B that need differeing steel, wood and plasctic. Its table is given below

Now clearly this a 2*3 matrix

The Supplier section has Comany C and Company D for which matrix is as below and is a 3*2 matrix:

(A) The final cost matrix will be of order 2*2.

For element 1 of cost matrix = R1*C1

=70*610+50*290+40*290=68800

For element 2 of cost matrix = R1*C2

=70*560+50*200+40*410=65600

For element 3 of cost matrix = R2*C1

=50*610+40*290+50*290=56600

For element 4 of cost matrix = R2*C2

=50*560+40*200+50*410=56500

The resulting Cost matrix is

(B)

Department A should use the company D, since the cost is lesser as compared to Company C by 3200

Department B should also use the company D, since the cost is lesser as compared to Company C by 100.

Steel Wood Plastic Department A 70 50 40 Department B 50 40 50

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