Production Volume $($units$)400$

$450$

$550$

$600$

$700$

$750$

Total Cost $($$$)$

$4000$

$5000$

$5400$

$5900$

$6400$

$7000$

Refer to exercise $21,$ where data on the production volume x and total cost y for a particu lar manufacturing operation were used to develop the estimated regression equation y$=1246\mathrm{.}67+7\mathrm{.}6$x$.$

a$.$ The company$$s production schedule shows that $500$ units must be produced next month. What is the point estimate of the total cost for next month?

b$.$ Develop a $99\%$ prediction interval for the total cost for next month.

c$.$ If an accounting cost report at the end of next month shows that the actual production cost during the month was $$6000,$ should managers be concerned about incurring such a high total cost for the month? Discuss.