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The last two problems in example 511 serve to

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Unformatted text preview: = 80, we get 150 = 0, which is impossible, so we conclude x that AC (x) > 80 for all x > 0. This means the average cost per system is always greater than $80 per system, but the average cost is approaching this amount as more and more systems are produced. Looking back at Example 2.1.5, we realize $80 is the variable cost per system − the cost per system above and beyond the fixed initial cost of $150. Another way to interpret our answer is that ‘infinitely’ many systems would need to be produced to effectively counterbalance the fixed cost. Our next example is another classic ‘box with no top’ problem. Example 4.3.3. A box with a square base and no top is to be constructed so that it has a volume of 1000 cubic centimeters. Let x denote the width of the box, in centimeters. Refer to the figure below. height depth width, x 1. Express the height h in centimeters as a function of the width x and state the applied domain. 2. Solve h(x) ≥ x and interpret. 3. Find and interpret the behavior of h(x) as x → 0+ and as x → ∞. 4. Express the surface area S of the box as a...
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