The below data on the production volume x and total cost y $($in dollars$)$ for a particular manufacturing operation were used to develop the estimated regression equation $=1\mathrm{.}497\mathrm{.}33+7\mathrm{.}28$x$.$ Production Volume $($units$)400450550600700750$ Total Cost $($$$)4,1005,1005,5006,0006\mathrm{.}4007,000($a$)$ The company's production schedule shows that $500$ units must be produced next month. What is the point estimate of the total cost $($in dollars$)$ for next month? $($Round your answer to the nearest cent.$)$ $ $5137\mathrm{.}33($b$)$ Develop a $99\%$ prediction interval for the total cost $($in dollars$)$ for next month. $($Round your answers to the nearest cent.$)$ $$-405\mathrm{.}53$ to $$5500($c$)$ If an accounting cost report at the end of next month shows that the actual production cost during the month was $$6,100,$ should managers be concerned about incurring such a high total cost for the month? Discuss. Since $$6,100$ is within the prediction interval, managers should not be concerned about incurring such a high total cost for one month.