A company with manufacturing plants located in State A and State B has​ labor-hour and wage requirements for the manufacture of three types of inflatable boats as given in the two matrices below. Complete parts​ (A) through​ (D).

**Hourly Wages**

​Labor-Hours **Per Boat**

**State A**

**State B**

**Cutting Dept**

**Assembly Dept**

**Packaging Dept**

17.5617.56

17.6917.69

Cutting Dept

0.50.5

0.40.4

0.20.2

​1-person boat

Nequals=

14.2214.22

14.5214.52

Assembly Dept

Mequals=

1.41.4

0.90.9

0.60.6

​2-person boat

9.579.57

11.4211.42

Packaging Dept

1.71.7

1.61.6

0.70.7

​4-person boat

Question content area bottom

Part 1

​(A) Find the labor costs for a​ one-person boat manufactured at the State A plant.

Labor

costsequals=​$enter your response here

To find the labor cost for a one-person boat manufactured at the State A plant, we need to calculate the total labor cost using the given hourly wages and the labor-hours required for each department.

Here’s how we can approach the problem step-by-step:

1. **Hourly Wages in State A:**
   - Cutting Department: $17.56
   - Assembly Department: $14.22
   - Packaging Department: $9.57

2. **Labor-Hours for a One-Person Boat:**
   - Cutting Department: 0.5 hours
   - Assembly Department: 1.4 hours
   - Packaging Department: 1.7 hours

Now, we calculate the labor cost for each department and sum them up.

### Labor Cost for Each Department:
- **Cutting Department**:  
  \[
  \text{Cost} = 17.56 \, \text{(hourly wage)} \times 0.5 \, \text{(hours)} = 8.78
  \]

- **Assembly Department**:  
  \[
  \text{Cost} = 14.22 \, \text{(hourly wage)} \times 1.4 \, \text{(hours)} = 19.91
  \]

- **Packaging Department**:  
  \[
  \text{Cost} = 9.57 \, \text{(hourly wage)} \times 1.7 \, \text{(hours)} = 16.27
  \]

### Total Labor Cost:
Now, sum up the costs for each department to find the total labor cost for a one-person boat manufactured at the State A plant:
\[
\text{Total Labor Cost} = 8.78 + 19.91 + 16.27 = 44.96
\]

Thus, the labor cost for a one-person boat at the State A plant is **$44.96**.

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Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the labor cost for a one-person boat manufactured at the State B plant?
2. How do the labor costs compare between the one-person and two-person boats in State A?
3. What are the labor costs for a four-person boat at the State A plant?
4. How would changes in the hourly wage in one department affect the overall labor cost?
5. What is the combined labor cost for manufacturing one boat of each type at the State A plant?

**Tip:** Always check unit consistency (hours, wages) when calculating labor costs!

A company with manufacturing plants located in State A and State B has labor-hour and wage requirements for the manufacture of three types of inflatable boats as given in the two matrices below. Complete parts (A) through (D). Part (A): Find the labor costs for a one-person boat manufactured at the State A plant.

This problem explains how to calculate the total labor cost for a one-person inflatable boat manufactured at a State A plant using matrix data for hourly wages and labor hours in the Cutting, Assembly, and Packaging departments. A step-by-step solution is provided to understand how costs are derived from the multiplication of hourly wages by department-specific labor hours.

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