The demand forecast for the next four periods is 90, 100, 120, and 140 units respectively. The plant has a regular capacity of 100 units per period, an overtime capacity of 10 units per period, and a subcontractor capacity of 5 units per period

There is a $5 per unit charge for regular production, an $8 per unit charge for overtime production, and a $9 per unit charge for subcontracting. The holding cost is $3 per unit per period, no shortages are allowed and the company has 5 units in inventory at the start of the planning period.
a. How many units should be produced using overtime?
b. How many units should be produced using subcontracting?
c. What is the total inventory holding cost?
d. What is the lowest total plan cost?
e. Fill out this table showing the number of units made by period using each type of production and the resulting inventory at the end of each period.

Period 1 Period 2 Period 3 Period 4 Total Cost
Forecast 90 100 120 140
Regular
Overtime
Subcontracting
Ending Inventory

a. 30 units made using overtime
b. 15 units made using subcontracting
c. $210 total holding cost (70 unit-periods)
d. $2585 total plan cost
e. table appears below:

Period 1 Period 2 Period 3 Period 4 Total Cost
Forecast 90 100 120 140
Regular ($5 ) 100 100 100 100 $2000
Overtime ($8 ) 0 10 10 10 $240
Subcontracting ($9 ) 0 5 5 5 $135
Ending Inventory ($3 ) 15 30 25 0 $210
$2585