The Austin, Texas plant of Computer Products produces disk units for personal and small business computers. Gerald Knox, the plant's production planning director, is looking over next year's sales forecast for these products and will be developing an aggregate capacity plan for the plant based on this forecast. The quarterly sales forecasts for the disk units are as follows:

Ample machine capacity exists to produce the forecast. Each disk unit takes an average of 20 labor-hours. In addition, you have collected the following information:

a. Inventory holding or carrying cost is $100 per disk unit per quarter. The holding cost is based on the inventory at the end of each quarter.

b. The plant works the same number of days in each quarter, 12 five-day weeks, 6 hours per day.

c. Beginning inventory is zero disk 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 price reduction is $300 per disk 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 filling orders, backlogged items will always be filled before current quarter items,

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 starting in the second 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 disk unit for the labor and you provide the material

i. Demand during the fourth quarter of the prior year was 1,980 units. 

j. Because there is a scheduled plant shut-down at the beginning of next year, the company wants to have the beginning inventory for next year at 360 units. This can be considered as additional fourth quarter demand. There will be no holding cost associated with these 360 units. 

k.  Assume that workers hired in any quarter will not need any training to reach full production in that quarter.

l. Compare the following three sales and operations plans.

i) Computer Products is considering a modified "matching" demand planning model for meeting the disk production. The company will hire and layoff workers to match the demand requirements each quarter as long as the capacity of the resulting workforce does not exceed 2,250 units per quarter. If it cannot meet the demand in a quarter because of this restriction, it will backlog the shortage until the next quarter. Ignoring the material cost, what is the total cost to produce the disks for the year? All workers will be fully utilized each quarter, in other words, there is no under utilization.

ii) As an alternative, the company will maintain a workforce capable of producing the demand during the fourth quarter of last year. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using straight time, the excess units will be outsourced. What is the total cost of this option, excluding the material cost?

iii) As an alternative, the company will establish in quarter one and then maintain a workforce capable of producing 2,160 units in a quarter. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using regular time labor, the excess units will be completed by using overtime, not to exceed 25% of the available straight time hours, and then backlogged until the next quarter when they will be produced using regular time labor. What is the total cost of this option, excluding the material cost?