Yu Amy Xia has developed a specialized airtight vacuum bag to extend the freshness of seafood shipped to restaurants. She has put together the following demand cost data: QUARTER FORECAST (UNITS) REGULAR TIME OVERTIME SUB-CONTRACT
1 500 400 80 100
2 750 400 80 100
3 900 800 160 100
4 450 400 80 100

Initial inventory = 250 units
Regular time cost = $1.00/unit
Overtime cost = $1.50/unit
Subcontracting cost = $2.00/unit
Carrying cost = $0.20/unit/quarter
Back order cost = $0.50/unit/quarter

Yu decides that the initial inventory of 250 units will incur the 20C/unit cost from each prior quarter (unlike the situation in most other companies, where a 0 unit cost is assigned).

a. Find the optimal plan using the transportation method.
b. What is the cost of the plan?
c. Does any regular time capacity go unused? If so, how much in which periods?
d. What is the extent of backordering in units and dollars?