The marginal cost of producing widgets is constant and modeled by the derivative…
MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
The marginal cost of producing widgets is constant and modeled by the derivative C′(q)=7dollars per widget, where q is the number of widgets produced. The fixed cost, the cost of producing zero widgets, is $1,200.
(a) Determine a formula for the total cost C(q) of producing q widgets, for q≥0. Clearly state all units involved.
(b) Describe, in complete sentences, why an arbitrary constant appears when C(q) is recovered from C′(q). Explain what this constant represents in the context of production costs.
(c) Suppose an analyst neglects to include the constant obtained in part (a). Explain qualitatively how this omission would affect the company’s cost estimates and give one potential managerial consequence.