Chapter 7.1, Problem 88E

(a)

To determine

To Graph: To graph the given log rules.

Explanation of Solution

Given information:Rate of interest in both funds and total interest earned.

Graph:

  

Interpretation:

In the above graph, x-axis represent the diameter of log in inches and y-axis represent the volume of the log. Scribner log rule shown in blue and Doyle log rule shown in green

(b)

To determine

To find: To find the diameter who satisfies the both rule

Answer to Problem 88E

When diameter is 24.71 or 3.86

Explanation of Solution

Given information:Given Scribner log rule and Doyle log rule

Formula used: Substitution method

Calculation:

Since the given rules are

  $\begin{array}{l}V={(}^D\mathrm{...}(1)\\ V=0.79D^2-2D-4\mathrm{...}(2)\\ $ {(D-4)}^2=0.79D^2-2D-4\text{from}(1)$D^2-8D+16=0.79D^2-2D-4\\ D^2-0.79D^2-8D+2D+16+4=0\\ 0.21D^2-6D+20=0\end{array}$

Using, quadratic formula

  $\begin{array}{l}D=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ D=\frac{-(-6)\pm \sqrt{{(-6)}^2-4\times 0.21\times 20}}{2\times 0.21}\\ D=\frac{6\pm \sqrt{36-16.8}}{0.42}\\ D=\frac{6\pm \sqrt{19.2}}{0.42}\\ D=\frac{6\pm 4.38}{0.42}\\ D=\frac{6+4.38}{0.42}\text{or}D=\frac{6-4.38}{0.42}\\ D=\frac{10.38}{0.42}\text{or}D=\frac{1.62}{0.42}\\ D=24.71\text{or}D=3.86\end{array}$

Hence when diameter is 24.71 or 3.86 the rules are agreed.

(c)

To determine

To Explain: Toexplain the rule apply for selling the given logs.

Answer to Problem 88E

The answer is Scribner log rule.

Explanation of Solution

Given information:Given Scribner log rule and Doyle log rule with graph

The Scribner log rule gives more volume than the Doyle log rule which can be clearly seen in the graph.

Therefore, with maximum volume the profit is also maximum for selling logs under the Scribner log rule.

Hence the Scribner log rule is applied.