# T. H. King Company

T. H. King Company

You may want to copy some data tables into Excel and conduct the analysis there.
1. The T. H. King Company has introduced a new product line that requires two work centers, A and B for manufacture. Work Center A has a current capacity of 10,000 units per year, and Work Center B is capable of 12,500 units per year. This year (year 0), sales of the new product line are expected to reach 10,000 units. Average growth is projected at an additional 1,000 units each year through year 5. Pre-tax profits are expected to be \$30 per unit throughout the 5-year planning period. Two alternatives are being considered:
#1)    Expand both Work Centers A and B at the end of year 0 to a capacity of 15,000 units per year, at a total cost for both Work Centers of \$200,000;
#2)    Expand Work Center A at the end of year 0 to 12,500 units per year, matching Work Center B, at a cost of \$80,000, then expanding both Work Centers to 15,000 units per year at the end of year 3, at an additional cost at that time of \$200,000.

a. Use the information in Table below. What is the pre-tax cash flow (net present value) for alternative #1 compared to the base case of doing nothing for the next 5 years? Please show your work in the following table.
TABLE  |   CASH FLOWS Projection – Alternative 1
Year    Projected Demand (units/yr)              Projected Overall Capacity (units/yr)                   Cash Inflow (outflow)

Projected Work Center A Cap    Projected Work Center B Cap            Investment Cost    Earning beyond Base Case
0    10,000
1    11,000
2    12,000
3    13,000
4    14,000
5    15,000

NPV = __________________________

b. What is the pre-tax cash flow (net present value) for alternative #2 compared to the base case of doing nothing for the next 5 years? Please show your work in the following table.

TABLE  |   CASH FLOWS Projection – Alternative 2
Year    Projected Demand (units/yr)              Projected Overall Capacity (units/yr)                   Cash Inflow (outflow)
Projected Work Center A Cap    Projected Work Center B Cap            Investment Cost    Earning beyond Base Case
0    10,000
1    11,000
2    12,000
3    13,000
4    14,000
5    15,000

NPV = __________________________

c. Based on your calculations in parts a) and b), what action, if any, should the Sharp Company take?  Moreover, if you could perform further decision analysis, is there another alternative any better than the existing ones, based on the information given so far?

d. The company’s operations manager (O) only projects that the demand grows an average of 1000 units/year to reach 13000 in year 3 but stays at13000 units in Years 4 and 5, as he is not so confident of the rosy forecast from M. If so, what would be your NPV results after performing analysis as in (a) and (b) above?

e. Please explain why (and how) NPVs determined in a) and b) should or should not be used as the main basis for your decision.

2. Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped.
Webster is concerned whether the filling process for tubes of caulking is in statistical control. Several samples of eight tubes are taken and each tube is weighed in ounces.

Tube Number
Sample    1    2    3    4    5    6    7    8    Avg    Range
1    7.98    8.34    8.02    7.94    8.44    7.68    7.81    8.11    8.040
2    8.23    8.12    7.98    8.41    8.31    8.18    7.99    8.06    8.160
3    7.89    7.77    7.91    8.04    8.00    7.89    7.93    8.09    7.940
4    8.24    8.18    7.83    8.05    7.90    8.16    7.97    8.07    8.050
5    7.87    8.13    7.92    7.99    8.10    7.81    8.14    7.88    7.980
Avgs

a. Assuming that taking only 5 samples is sufficient, please construct an x-bar chart and a R-chart by calculating the respective centerline, UCL and LCL. Based on both charts, is the process in statistical control? [That is, what is the conclusion on process variability and process average?] If not, which chart indicates a process out-of-control?

b. Sample 6 returns the following reading:
Tube Number
Sample    1    2    3    4    5    6    7    8    Avg    Range
6    8.13    8.14    8.11    8.13    8.14    8.12    8.13    8.14
Does Sample 6 indicate whether the process is control or not? Please explain.

3. The supervisor at the Precision Machine Shop wants to determine the staffing policy that minimizes total operating costs. The average arrival rate at the tool crib, where tools are dispensed to the workers, is eight machinists per hour (Lamda). Each machinist’s pay is \$20 per hour. The supervisor can staff the crib either with a junior attendant who is paid \$10 per hour and can process 10 arrivals (of machinists) per hour, or with a senior attendant who is paid \$18 per hour and can process 16 arrivals per hour. Assume both the arrival rate and the service rate follow Poisson distribution.
a. Please determine the operating characteristics of Tool Crib system under either the junior attendant or the senior attendant
Operating Characteristics    Junior attendant    Senior attendant

Average utilization of the attendant (U)
Average No. of machinists in the system (L), i.e., idle machinists
Average No. of machinists in line (Lq)
Average time (hour) spent in the system by a machinist (W)
Average waiting time (hour) in line by a machinist (Wq)

b. Please estimate the hourly operating cost of the system under each attendant. [Hint: Operating Costs Per Hour = Lamda * W * Machinist_Wage_Rate + Attendant_Wage_Rate.] Which attendant should be selected for the Tool Crib?

c. If the junior attendant is a fast learner and can achieve a service rate of 14 arrivals per hour after one month on the job, which attendant should be picked to staff the Tool Crib?

d. (newly added) At what service rate, would the junior attendant be picked over the senior in terms of hourly operating cost of the system?