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Chapter 8: Problem 90
What does a solid line mean in the graph of an inequality?
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Use the two steps for solving a linear programming problem, given in the box on page \(888,\) to solve the problems. In 1978 , a ruling by the Civil Aeronautics Board allowed Federal Express to purchase larger aircraft. Federal Express's options included 20 Boeing 727 s that United Airlines was retiring and/or the French-built Dassault Fanjet Falcon \(20 .\) To aid in their decision, executives at Federal Express analyzed the following data: $$\begin{array}{ll} {} & {\text { Boeing } 727 \quad \text { Falcon } 20} \\ {\text { Direct Operating cost }} & {\$ 1400 \text { per hour } \$ 500 \text { per hour }} \\ {\text { Payload }} & {42,000 \text { pounds } \quad 6000 \text { pounds }} \end{array}$$ Federal Express was faced with the following constraints: \(\cdot\) Hourly operating cost was limited to 35,000. \(\cdot\) Total payload had to be at least 672,000 pounds. \(\cdot\) Only twenty 727 s were available. Given the constraints, how many of each kind of aircraft should Federal Express have purchased to maximize the number of aircraft?
$$ \text { Let } f(x)=\left\\{\begin{aligned} x+3 & \text { if } x \geq 5 \\ 8 & \text { if } x<5 \end{aligned}\right. $$
Bottled water and medical supplies are to be shipped to survivors of an earthquake by plane. The bottled water weighs 20 pounds per container and medical kits weigh 10 pounds per kit. Each plane can carry no more than 80,000 pounds. If x represents the number of bottles of water to be shipped per plane and y represents the number of medical kits per plane, write an inequality that models each plane鈥檚 80,000-pound weight restriction.
A company that manufactures small canoes has a fixed cost of \(\$ 18,000 .\) It costs \(\$ 20\) to produce each canoe. The selling price is \(\$ 80\) per canoe. (In solving this exercise, let \(x\) represent the number of canoes produced and sold.)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed the solution set of \(y\) as \(x+2\) and \(x \geq 1\) without using test points.
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