A manufacturing plant produces two distinct products, A and B. The cost of producing one unit of A is $18 and that of B is $22. Assume that this plant incurs a weekly setup cost of $24,000 regardless of the number of units of A or B produced. The means and standard deviations of the weekly production levels of A and B are given in the S04_78.xlsx.
a. Assuming that the weekly production levels of A and B are independent, find the mean and standard deviation of this plant’s total weekly production cost. Between which two total cost figures can you be about 68% sure that this plant’s actual total weekly production cost will fall?
b. How do your answers in part a change if you discover that the correlation between the weekly production levels of A and B is actually 0.29? Explain the differences in the two sets of results.