A firm makes bulldozers (B), cranes (C) and tractors (T) at two locations, New York City (NYC) and Los Angeles (LA). The matrices below show the number of each item made in each location for the months of January (J) and February (F).

B C T
J = NYC 144 474 274
LA 598 572 302

B C T
F = NYC 424 492 546
LA 596 530 164

Required:
Suppose the production for March of all products at all locations was the average of the January and February production. Write an expression using the matrices J and F for the March production matrix M.

[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ C \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{284}&{483}&{410}\\{597}&{551}&{233}{2}}\\\end{array}\right][/tex]

Step-by-step explanation:

From the question we are told that

The number of each items made in the month of January[J] is

[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ C \ \ \ \ \ \ T\\J = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{144}&{474 }&{274}\\{598}&{572}&{302}\\\end{array}\right][/tex]

The number of each items made in the month of February[F] is

[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ C \ \ \ \ \ \ T\\J = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{ 424}&{492}&{546}\\{596 }&{530}&{164}\\\end{array}\right][/tex]

Generally given that the production for March of all products at all locations was the average of the January and February production then the number of each items made in the month of March[M] is

[tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ \ \ \ \ \ \ \ C \ \ \ \ \ \ \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{\frac{144 +424}{2}}&{\frac{474 +492}{2}}&{\frac{274 +546}{2}}\\{\frac{598 +596}{2}}&{\frac{572 +530}{2}}&{\frac{302+164}{2}}\\\end{array}\right][/tex]

=> [tex].\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B \ \ \ \ \ \ C \ \ \ \ \ T\\M = \left \ NYC} \atop {LA}} \right. \left[\begin{array}{ccc}{284}&{483}&{410}\\{597}&{551}&{233}{2}}\\\end{array}\right][/tex]