Final answer:
The total cost C of a manufacturer in a month, as a function of the number of widgets produced, is C(N) = Fixed Costs + (Variable Cost per Unit × N). For 250 widgets with a variable cost of $80 per widget and fixed costs of $160, the total cost is $20,160.
Step-by-step explanation:
To express the total cost C of a manufacturer in a month as a function of the number of widgets produced, we use the formula: C(N) = Fixed Costs + (Variable Cost per Unit × N), where N is the number of widgets. Assuming the fixed costs are $160 and the variable cost per unit is known, this formula can be applied.
For part b, if we know the variable cost per widget is $80, and the manufacturer produces 250 widgets, we can express the total cost function as C(250) = 160 + (80 × 250). To calculate the cost for 250 widgets, we multiply 80 by 250 and add the fixed costs of $160, which results in C(250) = 160 + 20000 = 20160.