Chapter 1.11, Problem 42P

a.

Summary Introduction

To determine: The values of $k$ and $a$ assuming $f\left(y\right)=k{y}^a$ as the relationship.

Introduction: From the past experiences, a big oil company can evaluate its present and the future costs. According to its study, each doubling of the size of a refinery at a single location results in the construction coststo about 68%.

b.

Summary Introduction

To determine: The best time to make additions in plant and the optimal size of each addition.

Introduction: Based on previous experiences, the oil company can easily predict the vivid picture of its present and future. Likewise, it can determine the optimal timing of plant additions and the optimal size of each addition too.

c.

Summary Introduction

To determine: The best timing to make additions in plant and the optimal size of each addition if the largest single refinery can be built with current technology is 15,000 barrels daily.

Introduction: When the major oil company installs the largest single refinery then its optimal size will not necessarily be huge while talking about the annual count. Similarly, the optimal timing of adding the plant will not necessarily be more always.