Chef Gourmet, Inc., has assembled the following data pertaining to its two most popular products.
Blender Food Processor
Direct material $ 18 $ 33
Direct labor 12 27
Manufacturing overhead @ $48 per machine hour 48 96
Cost if purchased from an outside supplier 60 114
Annual demand (units) 20,000 28,000
Past experience has shown that the fixed manufacturing overhead component included in the cost per machine hour averages $30. Management has a policy of filling all sales orders, even if it means purchasing units from outside suppliers.
Required:
1.
If 50,000 machine hours are available, and management desires to follow an optimal strategy, how many units of each product should the firm manufacture? How many units of each product should be purchased?
2.
With all other things constant, if management is able to reduce the direct material for a food processor to $18 per unit, how many units of each product should be manufactured? Purchased?
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To answer these questions, we need to calculate the total cost per unit for each product and compare it to the cost if purchased from an outside supplier.
1. To determine how many units to manufacture and purchase, we can use the concept of contribution margin.
a) Contribution margin per unit = selling price - total cost per unit.
For the blender:
- Direct material cost: $18
- Direct labor cost: $12
- Manufacturing overhead: $48 (calculated as $30 fixed overhead + $18 variable overhead)
Total cost per unit = $18 + $12 + $48 = $78
Contribution margin per unit = Selling price - Total cost per unit = $60 - $78 = -$18 (loss per unit)
For the food processor:
- Direct material cost: $33
- Direct labor cost: $27
- Manufacturing overhead: $96 (calculated as $30 fixed overhead + $66 variable overhead)
Total cost per unit = $33 + $27 + $96 = $156
Contribution margin per unit = Selling price - Total cost per unit = $114 - $156 = -$42 (loss per unit)
Based on the contribution margin per unit, both products result in a loss if manufactured. Therefore, it is more cost-effective to purchase both products from an outside supplier instead of manufacturing them.
b) To determine how many units to purchase, we need to calculate the total cost of purchasing the units.
For the blender:
Cost if purchased from an outside supplier: $60 per unit
Total cost of purchasing = Cost if purchased × Annual demand = $60 × 20,000 = $1,200,000
For the food processor:
Cost if purchased from an outside supplier: $114 per unit
Total cost of purchasing = Cost if purchased × Annual demand = $114 × 28,000 = $3,192,000
Therefore, to follow an optimal strategy, Chef Gourmet, Inc. should purchase 20,000 units of blenders and 28,000 units of food processors.
2. If the direct material cost for a food processor is reduced to $18 per unit, we need to recalculate the total cost per unit and contribution margin.
For the food processor:
New direct material cost: $18
Total cost per unit = $18 + $27 + $96 = $141
Contribution margin per unit = Selling price - Total cost per unit = $114 - $141 = -$27 (loss per unit)
Since the revised cost of the food processor still results in a loss per unit, it is still more cost-effective to purchase the food processors from an outside supplier. Therefore, the manufacturing quantity remains at 0, and 28,000 units of food processors should be purchased. The revised cost of the blender remains the same, so the optimal strategy would still be to purchase 20,000 units of blenders as well.