Matrix AB=C find C

Question

A HOUSING CONTACTOR HAS ORDERS FOR 4 ONE -BEDROOM UNITS, 10 TWO BEDDROOM UNITS AND 6 THREE BEDROOM UNITS. THE LABOR AND MATERIALS COSTS ( IN THOUSANDS OF DOLLARS) ARE GIVEN BY THE FOLLOWING:

.....................................1 BEDROOM.......................2BEDROOM.....................3BEDROOM

1. LABOR                     34                                        40                                    43
2. MATERIALS              50                                        60                                    67

A)....ORGANIZE THESE DATA INTO AN ORDER MATRIX CALLED  A and a cost matrix called B so that the ......."product", AB=C

B) find C

C) Interpret the meaning of each element of C 

 

Answer 1

A) Order matrix A = ( 4   10   6) is a  3X1 matrix

  Cost matrix  B = (34    50)

                           (40    60)

                           (43    67)    is  a 3X2 matrix

the Product matrix C is a 3X2 matrix

                             (34   50)

B) AB  = (4   10   6)(40   60)   = (4x34+10x40+6x43   4x50+10x60+6x67) =(794   1202) = C

                             (43   67)

 

C.) 794 is the total labor cost and 1202 is the total material cost.