Q 75. - Precalculus Enhanced with Graphing Utilities

Question

Minimum Average Cost: The average cost per hour in dollars, C, of producing $x$ riding lawn mowers can be modeled by the function $\overline{C}\left(x\right)=0.3x^2+21x-251+\frac{2500}{x}$.

(a) Use a graphing utility to graph $C = C\left(x\right)$.

(b) Determine the number of riding lawn mowers to produce

in order to minimize average cost.

(c) What is the minimum average cost?

Step-by-Step Solution

Answer

Part (a). The graph of the given function is shown below:

Part (b). The number of riding lawn mowers is $10 \text{mowers/hr}$.

Part (c). The minimum average cost is$239\text{/mowers}$.

Part (a). Step 1. Given information

The given function is $\overline{C}\left(x\right)=0.3x^2+21x-251+\frac{2500}{x}$.

Part (b) Step 2. Graph the given function by using graphic utility.

The graph of the given function is shown:

Part (b) Step 1. Find the number of riding lawn mowers to produce in order to minimize average cost.

From the graph, observe that the number of riding lawn mowers to produce in order to minimize average cost is $9.65 \text{mowers/hr} \approx 10 \mathrm{mowers}/\mathrm{hr}$.

Part (c) Step 1. Determine the minimum average cost.

From the graph, observe that the average cost is $238.6\text{/mowers}\approx 239\text{/mowers}$ when the number of riding lawn mowers is approximately $10 \text{mowers/hr}$.