A company with manufacturing plants located in Massachusetts and Virginia has labor-hour and wage requirements for the manufacture of three inflatable boats as given in the following two tables:

Let matrix L represent labor hours per boat and matrix W represent hourly wages.

a. Which product is undefined, L*W or W*L?

b. Find the product of the one that is defined.

c. Use your results from part b to find the labor costs of a one person boat manufactured in Massachusetts.

d. Label the rows and columns of the matrix in part b.

One Person boat Two person boat Three person boat Labor Hours per Boat Cutting Dept. 0.6 hr 1.0 hr 1.5 hr Assembly Dept. 0.6 hr 0.9 hr 1.2 hr Packaging Dept. 0.2 hr 0.3 hr 0.4 hr Cutting Dept. Assembly Dept. Packaging Dept. Hourly Wages MA $14 $12 $8 VA $10 $8 $7