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Sagot :
Let's go through the problem step-by-step to determine if Imperial Jewelers should accept the special order.
### Step 1: Analyzing the Costs
We are provided with several costs for manufacturing one bracelet:
- Direct materials: \[tex]$146 - Direct labor: \$[/tex]83
- Manufacturing overhead: \[tex]$32, of which \$[/tex]12 is variable and \[tex]$20 is fixed. For the special order, we have: - Selling price per bracelet: \$[/tex]361
- Special filigree increases materials cost by \[tex]$11 per bracelet. - Additional special tool cost: \$[/tex]456 (one-time cost, independent of the number of bracelets).
Given that most manufacturing overhead is fixed and unaffected, only the variable overhead cost is considered in the decision.
### Step 2: Calculate the Relevant Costs for the Special Order
Since fixed overheads do not change, we consider only variable costs and additional costs specific to this special order.
Let's break down the relevant cost of one bracelet with the special filigree:
- Direct materials cost per bracelet: \[tex]$146 - Additional material cost for filigree: \$[/tex]11
- Direct labor cost per bracelet: \[tex]$83 - Variable overhead per bracelet: \$[/tex]12
### Sum of Relevant Costs Per Bracelet:
Relevant cost per bracelet = Direct materials + Additional material cost + Direct labor + Variable overhead
= \[tex]$146 + \$[/tex]11 + \[tex]$83 + \$[/tex]12
= \[tex]$252 ### Step 3: Calculate Total Revenues from the Special Order The wedding party wants to buy 25 bracelets at the discounted price of \$[/tex]361 each.
Total revenue from the special order = Selling price per bracelet Number of bracelets
= \[tex]$361 25 = \$[/tex]9025
### Step 4: Calculate Total Relevant Cost of Fulfilling the Special Order
Total relevant cost per bracelet (including special filigree) = \[tex]$252 Special tool cost = \$[/tex]456 (one-time).
Total relevant cost = (Relevant cost per bracelet Number of bracelets) + Special tool cost
= (\[tex]$252 25) + \$[/tex]456
= \[tex]$6300 + \$[/tex]456
= \[tex]$6756 ### Step 5: Determine the Financial Advantage (Disadvantage) Financial advantage (disadvantage) = Total revenue - Total relevant cost = \$[/tex]9025 - \[tex]$6756 = \$[/tex]2269
### Step 6: Decision on Accepting the Special Order
The financial advantage of accepting the special order is \[tex]$2269. Since this is a positive amount, accepting the special order increases the company's profits by \$[/tex]2269.
### Summary
1. Financial advantage (disadvantage) of accepting the special order: \[tex]$2269 2. Should the company accept the special order? Yes, the company should accept the special order because it will be financially beneficial, increasing profits by \$[/tex]2269.
### Step 1: Analyzing the Costs
We are provided with several costs for manufacturing one bracelet:
- Direct materials: \[tex]$146 - Direct labor: \$[/tex]83
- Manufacturing overhead: \[tex]$32, of which \$[/tex]12 is variable and \[tex]$20 is fixed. For the special order, we have: - Selling price per bracelet: \$[/tex]361
- Special filigree increases materials cost by \[tex]$11 per bracelet. - Additional special tool cost: \$[/tex]456 (one-time cost, independent of the number of bracelets).
Given that most manufacturing overhead is fixed and unaffected, only the variable overhead cost is considered in the decision.
### Step 2: Calculate the Relevant Costs for the Special Order
Since fixed overheads do not change, we consider only variable costs and additional costs specific to this special order.
Let's break down the relevant cost of one bracelet with the special filigree:
- Direct materials cost per bracelet: \[tex]$146 - Additional material cost for filigree: \$[/tex]11
- Direct labor cost per bracelet: \[tex]$83 - Variable overhead per bracelet: \$[/tex]12
### Sum of Relevant Costs Per Bracelet:
Relevant cost per bracelet = Direct materials + Additional material cost + Direct labor + Variable overhead
= \[tex]$146 + \$[/tex]11 + \[tex]$83 + \$[/tex]12
= \[tex]$252 ### Step 3: Calculate Total Revenues from the Special Order The wedding party wants to buy 25 bracelets at the discounted price of \$[/tex]361 each.
Total revenue from the special order = Selling price per bracelet Number of bracelets
= \[tex]$361 25 = \$[/tex]9025
### Step 4: Calculate Total Relevant Cost of Fulfilling the Special Order
Total relevant cost per bracelet (including special filigree) = \[tex]$252 Special tool cost = \$[/tex]456 (one-time).
Total relevant cost = (Relevant cost per bracelet Number of bracelets) + Special tool cost
= (\[tex]$252 25) + \$[/tex]456
= \[tex]$6300 + \$[/tex]456
= \[tex]$6756 ### Step 5: Determine the Financial Advantage (Disadvantage) Financial advantage (disadvantage) = Total revenue - Total relevant cost = \$[/tex]9025 - \[tex]$6756 = \$[/tex]2269
### Step 6: Decision on Accepting the Special Order
The financial advantage of accepting the special order is \[tex]$2269. Since this is a positive amount, accepting the special order increases the company's profits by \$[/tex]2269.
### Summary
1. Financial advantage (disadvantage) of accepting the special order: \[tex]$2269 2. Should the company accept the special order? Yes, the company should accept the special order because it will be financially beneficial, increasing profits by \$[/tex]2269.
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