A juice company has found that the marginal cost of producing $x$ pints of fresh-squeezed orange juice is given by the function below, where $C^{\prime }(x)$ is in dollars. Approximate the total cost of producing 27.9 pt of juice, using 3 subintervals over $[0,279]$ and the left endpoint of each subinterval.
$$C^{\prime }(x)=0.000004x^2-0.002x+4,\text{ for }x\le 350$$
The total cost is about $\mathrm{\$}$
(Round the final answer to the nearest cent as needed. Round all intermediate values to the nearest thousandth as needed.)

Step 1 ：We are given the marginal cost function $C^{\prime }(x)=0.000004x^2-0.002x+4$, and we are asked to approximate the total cost of producing 27.9 pints of juice using the Left Riemann Sum method with 3 subintervals over the interval [0, 27.9].

Step 2 ：The Left Riemann Sum method divides the interval of integration into equal subintervals, and approximates the area under the curve on each subinterval by the area of a rectangle whose height is the value of the function at the left endpoint of the subinterval.

Step 3 ：We divide the interval [0, 27.9] into 3 equal subintervals, which gives us a width of approximately 9.3 for each subinterval.

Step 4 ：We calculate the value of $C^{\prime }(x)$ at the left endpoint of each subinterval, which gives us [4, 3.98174596, 3.96418384].

Step 5 ：We multiply each of these values by the width of the subintervals to get the area of the rectangles, and then sum these areas to get the total cost.

Step 6 ：The total cost of producing 27.9 pints of juice, approximated using the Left Riemann Sum method with 3 subintervals, is about $111.10. This is an approximation, and the actual cost may be slightly different.

Step 7 ：Final Answer: The total cost of producing 27.9 pints of juice is approximately $\boxed{{\displaystyle \mathrm{\$}111.10}}$.