Chapter 2.5, Problem 34E

a.

To determine

To write: a compound inequality that represents annual profits from 2006 to 2013.

Answer to Problem 34E

  $50\le P\le 90$

Explanation of Solution

Let P denotes the annual profits (in millions of dollar) from 2006 to 2013

From the given graph it can be observed that the least profit is 50 million dollar and maximum profit is 90 million dollar.

So, the compound inequality that represents annual profits from 2006 to 2013 is:

  $50\le P\le 90$

b.

To determine

if it is possible for company to have annual revenue of $ 160 million from 2006 to 2013.

Answer to Problem 34E

No

Explanation of Solution

From part (a), annual profits from 2006 to 2013 are given by the inequality $50\le P\le 90$ .

Also it is known that, Profit is the difference of the revenue and cost.

So, let P denotes the profit, R denotes the revenue and C denotes the cost. Then,

  $P=R-C$

So, the inequality from part (a) can be written as:

  $\begin{array}{c}50\le P\le 90\\ 50\le R-C\le 90\\ 50\le R-125\le 90\end{array}$

  $\begin{array}{c}50+125\le R\le 90+125\\ 175\le R\le 215\end{array}$

It implies that the company’s annual revenue from 2006 to 2013 is at least $175 million or at most $ 215 million.

Since $160 million doesn’t lie in this range. So, it is not possible for company to have annual revenue of $ 160 million from 2006 to 2013.