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Sagot :
Let's carefully analyze the data and determine the steps required to solve the problem.
Given:
- Current selling price per unit: \$52
- Current production costs per unit:
- Direct materials: \$14
- Direct labor: \$16
- Variable overhead: \$9
- Fixed overhead: \$9
To refine product quality and functionality, material and labor costs increase by 20%.
We need to determine:
a) The incremental profit or loss if the refined version of the product could be sold for \$57 per unit.
b) Whether the product should be processed further based on incremental profit or loss determined in part (a).
### Steps to determine the solution:
1. Calculate the increased material and labor costs:
- Incremental increase in material cost = 20% of direct materials
[tex]\[ \text{Incremental materials cost} = 0.20 \times 14 = 2.80 \][/tex]
- Incremental increase in direct labor cost = 20% of direct labor
[tex]\[ \text{Incremental labor cost} = 0.20 \times 16 = 3.20 \][/tex]
2. Calculate the new material and labor costs:
- New materials cost per unit
[tex]\[ \text{New materials cost} = 14 + 2.80 = 16.80 \][/tex]
- New labor cost per unit
[tex]\[ \text{New labor cost} = 16 + 3.20 = 19.20 \][/tex]
3. Calculate the initial and refined total production costs per unit:
- Initial total production cost per unit:
[tex]\[ \text{Initial cost} = 14 + 16 + 9 + 9 = 48 \][/tex]
- Refined total production cost per unit:
[tex]\[ \text{Refined cost} = 16.80 + 19.20 + 9 + 9 = 54.00 \][/tex]
4. Determine the incremental profit or loss:
- Initial profit per unit:
[tex]\[ \text{Initial profit} = 52 - 48 = 4 \][/tex]
- Refined profit per unit (selling price of refined product is \$57):
[tex]\[ \text{Refined profit} = 57 - 54 = 3 \][/tex]
- Incremental profit or loss:
[tex]\[ \text{Incremental profit or loss} = \text{Refined profit} - \text{Initial profit} = 3 - 4 = -1 \][/tex]
(This indicates a loss of \$1 per unit.)
### Conclusion:
a. The incremental profit or loss if Lakeside could sell the refined version of its product for \[tex]$57 per unit is a loss of \$[/tex]1.00.
b. Given that the incremental profit is actually a loss, Lakeside should not process the product further. Therefore:
[tex]\[ \text{Should it be processed further?} \quad \text{No} \][/tex]
Given:
- Current selling price per unit: \$52
- Current production costs per unit:
- Direct materials: \$14
- Direct labor: \$16
- Variable overhead: \$9
- Fixed overhead: \$9
To refine product quality and functionality, material and labor costs increase by 20%.
We need to determine:
a) The incremental profit or loss if the refined version of the product could be sold for \$57 per unit.
b) Whether the product should be processed further based on incremental profit or loss determined in part (a).
### Steps to determine the solution:
1. Calculate the increased material and labor costs:
- Incremental increase in material cost = 20% of direct materials
[tex]\[ \text{Incremental materials cost} = 0.20 \times 14 = 2.80 \][/tex]
- Incremental increase in direct labor cost = 20% of direct labor
[tex]\[ \text{Incremental labor cost} = 0.20 \times 16 = 3.20 \][/tex]
2. Calculate the new material and labor costs:
- New materials cost per unit
[tex]\[ \text{New materials cost} = 14 + 2.80 = 16.80 \][/tex]
- New labor cost per unit
[tex]\[ \text{New labor cost} = 16 + 3.20 = 19.20 \][/tex]
3. Calculate the initial and refined total production costs per unit:
- Initial total production cost per unit:
[tex]\[ \text{Initial cost} = 14 + 16 + 9 + 9 = 48 \][/tex]
- Refined total production cost per unit:
[tex]\[ \text{Refined cost} = 16.80 + 19.20 + 9 + 9 = 54.00 \][/tex]
4. Determine the incremental profit or loss:
- Initial profit per unit:
[tex]\[ \text{Initial profit} = 52 - 48 = 4 \][/tex]
- Refined profit per unit (selling price of refined product is \$57):
[tex]\[ \text{Refined profit} = 57 - 54 = 3 \][/tex]
- Incremental profit or loss:
[tex]\[ \text{Incremental profit or loss} = \text{Refined profit} - \text{Initial profit} = 3 - 4 = -1 \][/tex]
(This indicates a loss of \$1 per unit.)
### Conclusion:
a. The incremental profit or loss if Lakeside could sell the refined version of its product for \[tex]$57 per unit is a loss of \$[/tex]1.00.
b. Given that the incremental profit is actually a loss, Lakeside should not process the product further. Therefore:
[tex]\[ \text{Should it be processed further?} \quad \text{No} \][/tex]
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