Question

Two departments of a​ firm, A and​ B, need differing amounts of​ steel, wood, and plastic. The table below gives the amount of each product the departments need.

	Company C	Company D
Steel	600	560
Wood	280	190
Plastic	280	380

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	Wood	Plastic
Department A	80	60	30
Department B	60	30	60

a) Use matrix multiplication to determine how much these orders will cost each department at each of the two suppliers. Enter the amounts into the cost matrix shown on the right. Co. C Co. D Dept. A ____ ____ Dept. B   ____ ____ b. From which supplier should each department make its​ purchase? Which company should department A​ use? Company C or Company D? Which company should department B​ use? Company C or Company D?

Answer 1

department A needs steel 80 units , wood 60 units , plastic 30 units

department B needs steel 60 units, wood 30 units, plastic 60 units

there are two suppliers C and D with cost per unit by supplier C is

steel- 600 , wood-280, plastic- 280

and cost per unit by supplier D is

steel-560 wood-190 plastic -380

a) let matrix X denotes the demand of the two departments of different raw materials with rows defining the departments and columns defining the raw materials needed

X=

matrix Y denotes the cost per units by suppliers with rows defining the raw materials and columns defining the suppliers

Y=

then the matrix XY would give the cost the departments have to pay to the suppliers with rows defining the departments and columns defining the suppliers

(1,1) element of XY is=80*600+60*280+30*280=73200

(1,2) element of XY is=80*560+60*190+30*380=67600

(2,1) element of XY is=60*600+30*280+60*280=61200

(2,2) element of XY is =60*560+30*190+60*380=62100

so,

Co. C Co. D

dept A 73200 67600

dept B 61200 62100

b)department A should use company D as it is cheaper

department B should use company C as it is cheaper.