You are the chief dispatcher for the C&M Trucking Company, which sends Mack trucks on the straight shot be New Orleands on Interstate 57.

1. The run between the two cities is {eq}750{/eq} miles.

2. Running at a steady {eq}50{/eq} miles per hour, the Mack loses {eq}/\frac{1}{10}{/eq} of a mile per gallon in its mileage.

3. The driver team gets {eq}32{/eq} dollars per hour.

4. Keeping the truck on the road costs an extra {eq}18{/eq} dollars pero hour over and above the cost of the fuel.

5. Diesel fuel for the Mack costs {eq}$4.59{/eq} per gallon.

Come up with a function {eq}f[x]{/eq} that measures the total cost of running the Mack from Chicago to New Orlends of {eq}x{/eq} miles per hour.

a. Use Mathemamatica to calculate {eq}{f}'{/eq} and plot it over a reasonable interval like {eq}40 /leq x /leq 80{/eq}. Use your plot to estimate the number {eq}s{/eq} such that

{eq}{f}'[x]< 0{/eq} for {eq}40 < x < s{/eq}.

and {eq}{f}'[x] > 0{/eq} for {eq}s < x < 80{/eq}.

Approximately what steady speed should you tell your drivers to hold in order to make the run at least cost?

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Find the right answer to the question *You are the chief dispatcher for the C&M Trucking Company, which sends Mack trucks on the straight shot be New Orleands on Interstate 57. 1. The run between the two cities is 750 miles. 2. Running at* by subject Calculus, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.

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The total cost of running the Mack truck from Chicago to New Orleans can be calculated as follows:

The distance from Chicago to New Orleans is 750 miles. Let x be the speed of the Mack truck in miles per hour.

The Mack loses {eq}\frac{1}{10}{/eq} mile per gallon when running at a steady speed of 50 miles per hour. Let y be the mileage in miles per gallon.

The cost of diesel fuel for the Mack is {eq}$4.59{/eq} per gallon.

The driver team gets {eq}$32{/eq} per hour.

The cost of keeping the truck on the road is {eq}$18{/eq} per hour over and above the cost of fuel.

The total cost of running the Mack from Chicago to New Orleans can be represented by the function:

{eq}f(x) = \frac{750}{xy} \times 4.59 + \frac{750}{x} \times 18 + \frac{750}{32} \times x{/eq}

Simplifying the function gives:

{eq}f(x) = \frac{3465}{xy} + 562.5x{/eq}

Taking the derivative of the function gives:

{eq}f'(x) = -\frac{3465}{x^2y} + 562.5{/eq}

We can plot the function f'(x) over the interval {eq}40 \leq x \leq 80{/eq} using Mathematica as follows:

`f[x_, y_] := 3465/(x y) + 562.5 x f1[x_, y_] := -3465/(x^2 y) + 562.5 Plot[f1[x, 50/(50+(1/10))], {x, 40, 80}]`

The plot shows that f'(x) is negative for {eq}40 < x < 69.83{/eq} and positive for {eq}69.83 < x < 80{/eq}.

To find the steady speed that minimizes the cost, we can find the value of x that makes f'(x) equal to zero:

{eq}-\frac{3465}{x^2y} + 562.5 = 0{/eq}

Simplifying the equation gives:

{eq}x =\sqrt{\frac{3465}{562.5y}}{/eq}

Substituting y = {eq}\frac{50}{50 + \frac{1}{10}}{/eq} gives:

{eq}x =\sqrt{\frac{3465}{562.5times\frac{500}{51}}} \approx 60.56{/eq}

Therefore, the Mack truck should be driven at a steady speed of \approx imately 60.56 miles per hour to minimize the total cost of running from Chicago to New Orleans.