An automobile maker has two assembly plants at which cars with either 4, 6, or 8 cylinders and with either standard or automatic transmission are assembled. The annual production at the first plant of cars with the number of cylinders–transmission type (standard, automatic) is as follows:

4: 12,000, 15,000; 6: 24,000, 8000; 8: 4000, 30,000

At the second plant the annual production is

4: 15,000, 20,000; 6: 12,000, 3000; 8: 2000, 22,000

Set up matrices for this production, and by matrix addition find the matrix for the total production by the number of cylinders and type of transmission.