two manufacturing plants in Massachusetts (MA) and Virginia (VA) has different labor-hour and wage requirements for manufacturing 3 types of boats. Matrix M shows the labor-hour of 3 types of boats. Matrix N shows the wage requirements of each type of labor in the two plants in MA and VA.Labor-hours per boatM=cutting departmentassembly departmentpackaging department 0.6 hr0.6 hr0.2hrone-person boat1.0hr0.9hr0.3hrtwo-person boat1.5hr1.2hr0.4hrfour-person boathourly wagesN=MAVA $17.30$14.65cutting department$12.22$10.29Assembly department$10.63$9.66packaging departmentA) find the total labor cost for a one-person boat manufactured at the Massachusetts plant?B)find the total labor cost for a four-person boat manufactured at the Virginia plant?C)find MN. Label the rows and the columns in the resulting matrix.

Given: Matrix M=0.60.60.210.90.31.51.20.4Matrix N=17.3014.6512.2210.2910.639.66We first multiply the…

Answered: two manufacturing plants in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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two manufacturing plants in Massachusetts (MA) and Virginia (VA) has different labor-hour and wage requirements for manufacturing 3 types of boats. Matrix M shows the labor-hour of 3 types of boats. Matrix N shows the wage requirements of each type of labor in the two plants in MA and VA.

Labor-hours per boat

cutting department	assembly department	packaging department
0.6 hr	0.6 hr	0.2hr	one-person boat
1.0hr	0.9hr	0.3hr	two-person boat
1.5hr	1.2hr	0.4hr	four-person boat

hourly wages

MA	VA
$17.30	$14.65	cutting department
$12.22	$10.29	Assembly department
$10.63	$9.66	packaging department

A) find the total labor cost for a one-person boat manufactured at the Massachusetts plant?

B)find the total labor cost for a four-person boat manufactured at the Virginia plant?

C)find MN. Label the rows and the columns in the resulting matrix.

Expert Solution

Step 1

$G i v e n : M a t r i x M = [\begin{matrix} 0.6 & 0.6 & 0.2 \\ 1 & 0.9 & 0.3 \\ 1.5 & 1.2 & 0.4 \end{matrix}] M a t r i x N = [\begin{matrix} 17.30 & 14.65 \\ 12.22 & 10.29 \\ 10.63 & 9.66 \end{matrix}] W e f i r s t m u l t i p l y t h e m a t r i c e s M N C o n s i d e r M N = [\begin{matrix} 0.6 & 0.6 & 0.2 \\ 1 & 0.9 & 0.3 \\ 1.5 & 1.2 & 0.4 \end{matrix}] [\begin{matrix} 17.30 & 14.65 \\ 12.22 & 10.29 \\ 10.63 & 9.66 \end{matrix}] = [\begin{matrix} 0.6 \times 17.30 + 12.22 \times 0.6 + 0.2 \times 10.63 & 0.6 \times 14.65 + 0.6 \times 10.29 + 0.2 \times 9.66 \\ 1 \times 17.30 + 0.9 \times 12.22 + 0.3 \times 10.63 & 1 \times 14.65 + 0.9 \times 10.29 + 0.3 \times 9.66 \\ 1.5 \times 17.30 + 1.2 \times 12.22 + 0.4 \times 10.63 & 1.5 \times 14.65 + 1.2 \times 10.29 + 0.4 \times 9.66 \end{matrix}] = [\begin{matrix} 19.838 & 16.896 \\ 31.487 & 26.809 \\ 44.866 & 38.187 \end{matrix}]$

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