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If the manufacturer of the fine pens is minimizing costs, it will produce the 60 pens at the first plant, incurring a total cost of $3,900, which is detailed as follows:
Variable costs = $3,600 (60 x 60)
Fixed costs at first plant = $100
Fixed costs at second plant (opportunity costs) = $200
Data and Calculations:
Total production cost in first plant = TC1 = y₁²+ 100.
Total production cost in second plant = TC2=y₂³ +200
Where:
y₁ = number of pens produced in the first plant
y₂ = number of pens produced in the second plant
Total cost of producing at the first plant = $3,900 (60² + 100) + 200
Total cost of producing at the second plant = $216,200 (60³ + 200)
Thus, if the firm produces 60 fine pens, and wants to minimize costs, it will produce the 60 fine pens at the first plant with a total cost of $3,900 (60² + 100) + 200, instead of producing the 60 fine pens at the second plant with a total cost of $216,200 (60³ + 200) or even any part of the fine pens.
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