Tagway 4000 is a computer manufacturer based in Montana. One component of the computer is an internal battery that keeps track of the time and date while the computer is turned off. Tagway produces the batteries in- house. The division that produces the batteries (one million each year) is treated as a cost center. The manager of the division is compensated based on her ability to keep total costs low and meet quality control measures of numbers of defects and delivery time. She has a base salary of $ 144,000. She is eligible for a $ 34,000 bonus if total costs do not exceed $ 2 million, not including her compensation. She is eligible for a $ 40,000 bonus if there are 32 or fewer defects per one million units produced. Finally, she is eligible for a $ 22,000 bonus if she delivers batteries on time. On time is defined as averaging two days between the order from the assembly department and delivery to the assembly department.

The basic cost of producing a battery is $ 1.55. However, current methods have an inherent defect rate of 1,032 defects per million (approximately four standard deviations or 4 sigma). The cost of improving the defect rate involves using higher- quality materials and more experienced labor. Down to 32 defects per million (approximately 5 sigma) the costs are linear. (Based on currently available inputs, improving the defect rate below 32 per million is impossible.) For every additional $ 450, one defect per million can be removed. In other words, the cost to reduce defects to the desired level of 32 per million is $ 450,000.

The current production method delivers the batteries in an average of four days. The cost of overtime necessary to lower the average to three days is $ 90,000. The cost of speeding up delivery another day is $ 95,000, making the cumulative cost of lowering the average to two days $ 185,000. The marginal cost of reducing the average delivery a third day is $ 115,000, making the total cost of reducing the average delivery time to one day $ 300,000.

Required:

a. Create a table showing the production costs for defect rates of 1,032; 500; 100; 50; and 32 per million and average delivery times of one to four days. Do not include the manager’s salary. Note the minimum cost.

b. Create a table showing the manager’s compensation for defect rates of 1,032; 500; 100; 50; and 32 and average delivery times of one to four days.

c. Comment on the ideal number of defects and delivery times necessary to achieve the minimum costs and the maximum compensation level.

d. Assume that the company as a whole can measure the financial losses related to defects and late deliveries. The costs would include warranty costs, express delivery charges, lost sales, and lost goodwill. These costs do not affect the manager’s compensation. The cost for each defect is $ 460. The cost for each day above one- day average delivery is $ 500,000 per day late. That is $ 0 for one- day average delivery, $ 500,000 for two days, and so on. Create a table showing the firm’s total costs— including production costs, costs of defects, costs of delays, and the cost of the manager’s compensation (including applicable bonus)—for defect rates of 1,032; 500; 100; 50; and 32 per million and average delivery times of one to four days.

e. Comment on the optimum delivery times and number of defects necessary to achieve the minimum costs to the firm and the maximum compensation level now that the firm’s total costs are considered.