A Study of the Costs to Produce Airplanes in World $M C(x)=M M_{0} x^{\log _{2} 0.9}$

question 8

Short Answer

A study of the costs to produce airplanes in World War II led to the theory of "learning curves," the idea of which is that the marginal cost per plane decreases over the duration of a production run.In other words, with experience, staff on an assembly line can produce planes with greater efficiency.The 90% learning curve describes a typical situation where the marginal cost, MC, to produce the x^th plane is given by $M C(x)=M M_{0} x^{\log _{2} 0.9}$ , where $M_{0}$ = marginal cost to produce the first plane.[Note: You may use the fact that $\log _{2} x=\frac{\ln x}{\ln 2}$ .] If a plant produces planes with a 90% learning curve on production costs, and the marginal cost for the first plane is $700,000, then what is the marginal cost to produce the fourth plane? Round to the nearest thousand dollars.

---

Definitions:

Inoperable Melanoma

A stage of melanoma cancer that cannot be surgically removed due to its location, size, or the patient's health, often requiring alternative treatments.

Elisabeth Kübler-Ross

A Swiss-American psychiatrist known for her work on death and dying, and for proposing the theory of the Five Stages of Grief.

Emotion

Emotion refers to a complex psychological state that involves an experiential, physiological, and behavioral response to a personally significant situation.

Menopause

The period that marks the end of a woman’s menstrual cycles, typically occurring in middle age, signifying the end of reproductive years.