Chapter 1 - Section 1.3 - Operations on Real Numbers and Order of Operations - Exercise Set: 97b

As the number of bookshelves manufactured increases, the cost per bookshelf decrease. This is because the denominator increases proportionally faster than the numerator. Also, the production cost per unit is known to decrease as more units are manufactured.

Work Step by Step

From part (a) we have: $\begin{array}{ccccc} \\x &10 &100 &1000 \\\\\dfrac{100x+5000}{x} &600 &150 &105 \end{array}$ Based on the values in the table above, the cost per bookshelf, which is represented by $\dfrac{100x+5000}{x}$, decreases as the number of bookshelves manufactured (represented by $x$) increases. Based on the given expression, the value of $\dfrac{100x+5000}{x}$ decreases as $x$ increases because the denominator increases proportionally faster than the numerator. Industry-wise (situation-wise), the cost per bookshelf decreases because the cost of production gets smaller as more bookshelves are manufactured.

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