Problems:
Matrix and word problem
A contractor employs carpenters, electricians, and plumbers, working three shifts per day. The number of labor-hours required for carpenters in shift 1 is 40 hours, electricians in shift 1 is 28 hours, and plumbers in shift 1 is 9 hrs. The number of labor-hours required for carpenters in shift 2 is 18 hours, electricians in shift 2 is 32 hours, and plumbers in shift 2 is 15 hours. The number of labor-hours required for carpenters in shift 3 is 10 hours, electricians in shift 3 is 15 hours, and plumbers in shift 3 is 5 hours. Labor in shift 1 costs $11.00 per hour, shift 2 $12.50 per hour, and shift 3 $13.90 per hour.
Write a matrix A that denotes the amount of labor-hours based on shifts and each type of labor (carpenter, electrician, or plumber).
Write a column vector B representing labor costs per shift.
Perform the multiplication AB and explain what this product represents.