Jan Kottas is the owner of a small company that buys and resells electric knives used to cut fabric. The annual demand is for 8,000 knives, and Jan is currently buying from Knives-R-Us. The ordering cost is $100 per order. The carrying cost per year is 4% of the acquisition cost of the knife, which is $20.00.
Jan has been approached by Knives-R-Us about buying knives under a new pricing schedule. One option is to order the knives in quantities between 1400 and 1599. If she does this, Knives-R-Us will lower the acquisition price to $19.75 each. If she buys 1600 or more at a time, the company will lower the price to $19.50. Of course, for all other quantities she can still buy the knives at $20.00 per knife.
If your order quantities are in fraction of units, please leave them as such.
a) Considering the total cost, composed of the holding cost and ordering cost and including the acquisition cost of the knives, how many should she buy per order to realize the lowest total cost?
b) Provide the lowest total cost for each of the three price options: $19.50, $19.75, and $20.00. Include the holding, ordering and acquisition cost.
2. (30 points)
The Austin, Texas plant of Computer Products produces external hard drives for personal and small business computers. Gerald Knox, the plant’s production planning director, is looking over next year’s sales forecasts for these products and will be developing an aggregate capacity plan for the plant. The quarterly sales forecasts for the external hard drives are as follows:
|1st Quarter||2nd Quarter||3rd Quarter||4th Quarter|
Ample machine capacity exists to produce the forecast. Each external hard drive takes an average of 20 labor-hours. In addition, you have collected the following information:
a. Inventory carrying cost is $100 per external hard drive per quarter. The cost is applied to all units in inventory at the end of a quarter.
b. The plant works the same number of days in each quarter, 12 five-day weeks, 6 hours per day.
c. For several reasons, there is a shortage of 300 units carried over from last year and these units must be provided during the first quarter. There is no holding or backlog costs associated with these 300 units.
d. In a backlog situation, the customer will wait for his order to be filled but will expect a price reduction each quarter he waits. The backlog costs are $300 per external hard drive for the first quarter the customer waits, $700 for the second quarter the customer waits, and $900 for the third quarter the customer waits. In any quarter, if there is a backlog, this backlog will be filled before the demand for that period is filled.
e. The cost of hiring a worker is $800 while the cost of laying off a worker is $950.
f. The straight time labor rate is $20 per hour for the first quarter and increases to $22 per hour in the fourth quarter.
g. Overtime work is paid at time and a half (150%) of the straight time work.
h. Outsourcing (contract work) is paid at the rate of $475 per external hard drive for the labor and you provide the material.
i. Demand is projected to increase this year. Demand during the fourth quarter of the prior year was 2,340 units. The demand for the first quarter of the next year (year following the year you are analyzing) is projected to be at the 2,700 unit level.
j. Assume that individuals hired in a quarter are capable of working at the100% production level if the demand is requires it..