Answer :
Let's break down the solution step by step for determining an economical sales and production mix for the coming year at Walton Toy Company, based on the given data.
### Step 1: Gather the given data
The essential data provided are:
1. Demand for next year, selling price, direct material cost per unit, and direct labor cost per unit for each product:
| Product | Demand Next year (units) | Selling Price per Unit ([tex]$) | Direct Material per Unit ($[/tex]) | Direct Labor per Unit (hours) |
|------------|---------------------------|----------------------------|------------------------------|--------------------------------|
| Debbie | 50,000 | 16.70 | 4.30 | 6.40 |
| Trish | 42,000 | 7.50 | 1.10 | 4.00 |
| Sarah | 35,000 | 26.60 | 6.44 | 11.20 |
| Mike | 40,000 | 14.00 | 2.00 | 8.00 |
| Sewing kit | 325,000 | 9.60 | 3.20 | 3.20 |
2. Additional data for labor and overheads:
- Direct labor rate: [tex]$16 per hour - Plant capacity: 130,000 direct labor-hours per year - Fixed manufacturing costs: $[/tex]520,000 per year
- Variable overhead cost: [tex]$2 per direct labor-hour - Nonmanufacturing costs are fixed - Finished goods inventory is negligible ### Step 2: Calculate the total variable cost per unit for each product The variable costs include direct material cost per unit, direct labor cost per unit, and variable overhead cost per unit. The calculation is as follows: #### For each product calculate: 1. Direct Labor Cost per Unit: \[ \text{Direct labor cost per unit} = \text{Direct labor per unit (hours)} \times \text{Direct labor rate} \] 2. Variable Overhead Cost per Unit: \[ \text{Variable Overhead per unit} = \text{Direct labor per unit (hours)} \times \text{Variable overhead rate} \] 3. Total Variable Cost per Unit: \[ \text{Total variable cost per unit} = \text{Direct material per unit} + \text{Direct labor cost per unit} + \text{Variable overhead per unit} \] ### Step 3: Determine Contribution Margins per Unit The contribution margin per unit is calculated by subtracting the total variable cost per unit from the selling price per unit. ### Step 4: Summarize findings into a table Let's put all that information into a table directly from the given solution: | Product | Selling Price per Unit ($[/tex]) | Direct Material per Unit ([tex]$) | Direct Labor per Unit (hours) | Total Variable Cost per Unit ($[/tex]) | Contribution Margin per Unit ($) | Labor Hours Needed per Unit |
|------------|----------------------------|------------------------------|--------------------------------|----------------------------------|---------------------------------|------------------------------|
| Debbie | 16.70 | 4.30 | 6.40 | 119.50 | -102.80 | 6.4 |
| Trish | 7.50 | 1.10 | 4.00 | 73.10 | -65.60 | 4.0 |
| Sarah | 26.60 | 6.44 | 11.20 | 208.04 | -181.44 | 11.2 |
| Mike | 14.00 | 2.00 | 8.00 | 146.00 | -132.00 | 8.0 |
| Sewing kit | 9.60 | 3.20 | 3.20 | 60.80 | -51.20 | 3.2 |
### Step 5: Interpret the Data
Based on the data:
1. All products have a negative contribution margin per unit; producing any of them results in a loss per unit.
2. Debbie has the least negative contribution margin and requires the most labor hours per unit.
Given this situation, it might be necessary to reassess other costs, pricing strategies, or explore other product mixes. However, considering the numbers, we should recommend focusing on improving processes or revisiting the pricing strategy as producing these products as is will lead to financial losses.
### Step 1: Gather the given data
The essential data provided are:
1. Demand for next year, selling price, direct material cost per unit, and direct labor cost per unit for each product:
| Product | Demand Next year (units) | Selling Price per Unit ([tex]$) | Direct Material per Unit ($[/tex]) | Direct Labor per Unit (hours) |
|------------|---------------------------|----------------------------|------------------------------|--------------------------------|
| Debbie | 50,000 | 16.70 | 4.30 | 6.40 |
| Trish | 42,000 | 7.50 | 1.10 | 4.00 |
| Sarah | 35,000 | 26.60 | 6.44 | 11.20 |
| Mike | 40,000 | 14.00 | 2.00 | 8.00 |
| Sewing kit | 325,000 | 9.60 | 3.20 | 3.20 |
2. Additional data for labor and overheads:
- Direct labor rate: [tex]$16 per hour - Plant capacity: 130,000 direct labor-hours per year - Fixed manufacturing costs: $[/tex]520,000 per year
- Variable overhead cost: [tex]$2 per direct labor-hour - Nonmanufacturing costs are fixed - Finished goods inventory is negligible ### Step 2: Calculate the total variable cost per unit for each product The variable costs include direct material cost per unit, direct labor cost per unit, and variable overhead cost per unit. The calculation is as follows: #### For each product calculate: 1. Direct Labor Cost per Unit: \[ \text{Direct labor cost per unit} = \text{Direct labor per unit (hours)} \times \text{Direct labor rate} \] 2. Variable Overhead Cost per Unit: \[ \text{Variable Overhead per unit} = \text{Direct labor per unit (hours)} \times \text{Variable overhead rate} \] 3. Total Variable Cost per Unit: \[ \text{Total variable cost per unit} = \text{Direct material per unit} + \text{Direct labor cost per unit} + \text{Variable overhead per unit} \] ### Step 3: Determine Contribution Margins per Unit The contribution margin per unit is calculated by subtracting the total variable cost per unit from the selling price per unit. ### Step 4: Summarize findings into a table Let's put all that information into a table directly from the given solution: | Product | Selling Price per Unit ($[/tex]) | Direct Material per Unit ([tex]$) | Direct Labor per Unit (hours) | Total Variable Cost per Unit ($[/tex]) | Contribution Margin per Unit ($) | Labor Hours Needed per Unit |
|------------|----------------------------|------------------------------|--------------------------------|----------------------------------|---------------------------------|------------------------------|
| Debbie | 16.70 | 4.30 | 6.40 | 119.50 | -102.80 | 6.4 |
| Trish | 7.50 | 1.10 | 4.00 | 73.10 | -65.60 | 4.0 |
| Sarah | 26.60 | 6.44 | 11.20 | 208.04 | -181.44 | 11.2 |
| Mike | 14.00 | 2.00 | 8.00 | 146.00 | -132.00 | 8.0 |
| Sewing kit | 9.60 | 3.20 | 3.20 | 60.80 | -51.20 | 3.2 |
### Step 5: Interpret the Data
Based on the data:
1. All products have a negative contribution margin per unit; producing any of them results in a loss per unit.
2. Debbie has the least negative contribution margin and requires the most labor hours per unit.
Given this situation, it might be necessary to reassess other costs, pricing strategies, or explore other product mixes. However, considering the numbers, we should recommend focusing on improving processes or revisiting the pricing strategy as producing these products as is will lead to financial losses.
