Chapter 1 - Section 1.10 - Modeling with Functions - Exercise Set - Page 293: 30

The expression of cost to enclose the rectangular garden in terms of one of the dimensions $x$ is $C\left( x \right)=29x+\frac{5000}{x}$.

Work Step by Step

Let the length of the garden be x and breadth of the garden be $y$. Write the expression for the area of the rectangular garden. $xy=125$ Calculate y in terms of x. $y=\frac{125}{x}$ Write the expression for the cost of building three brick walls around the garden which costs $\$20\text{perfoot}$and fencing around one side which costs$\$9\text{perfoot}$ $C=20\left( x+2y \right)+9x$ Substitute $\frac{125}{x}$ for $y$. \begin{align} & C=20\left[ x+2\left( \frac{125}{x} \right) \right]+9x \\ & =20x+\frac{5000}{x}+9x \\ & =29x+\frac{5000}{x} \end{align} The cost is function of x, so it can be expressed as, $C\left( x \right)=29x+\frac{5000}{x}$ Hence, expression of cost to enclose the rectangular garden in terms of one of the dimensions $x$ is $C\left( x \right)=29x+\frac{5000}{x}$.

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