Question

unless an additional fee is paid, some airlines will not check any luggage for which the sum of the items length, width, and height exceeds 85 in. a shipping company will ship a package only if the sum of the packages length and girth (distance around its mid - section) does not exceed 200 in. a promotion company is ordering several 60 - in. long cases that will be both mailed and checked as luggage. using w and h for the width and height (in inches), respectively, write and graph an inequality that represents all acceptable combinations of width and height. click the icon to view the figure. the inequality that must be satisfied by the width and height is (simplify your answer. type an inequality.)

Explanation:

Step1: Consider airline - check requirement

The length of the case is 60 in. For airlines, the sum of length, width \(w\), and height \(h\) should not exceed 85 in. So, \(60 + w+h\leqslant85\).

Step2: Consider shipping - company requirement

The girth is \(2(w + h)\) and the length is 60 in. For the shipping company, \(60+2(w + h)\leqslant200\).

Step3: Simplify the first inequality

From \(60 + w+h\leqslant85\), we get \(w + h\leqslant85 - 60\), which simplifies to \(w + h\leqslant25\).

Step4: Simplify the second inequality

From \(60+2(w + h)\leqslant200\), first subtract 60 from both sides: \(2(w + h)\leqslant200 - 60=140\). Then divide both sides by 2, we get \(w + h\leqslant70\).
Since \(w + h\leqslant25\) is more restrictive than \(w + h\leqslant70\), the inequality that represents all acceptable combinations of width and height is \(w + h\leqslant25\) with \(w\geqslant0\) and \(h\geqslant0\) (because width and height cannot be negative).

Answer:

\(w + h\leqslant25,w\geqslant0,h\geqslant0\)