Problem. p73 2-14
Wonka Widget Inc.
3-period inventory planning problem
Question: how many to produce at each period to minimize total cost ?
Decision Variables: units of widgets to prduce each period
Xi -- units produced in period i
e.g. X2 -- units of widgets produced in period 2
Objective: min Manufacturing cost + Inventory cost
Constraints: demand must be satisfied

The formulation is as follows:
Min 2x1+4x2+3x3+ I1 + I2
Constraints:
Period 1: X1 - I1 = 10000
Period 2: I1 + X2 - I2 = 20000
Period 3: I2 + X3 =30000
X1>=0, X2>=0 , X3>=0, I1>=0, I2>=0

Problem. p76 2-23.
Data: time requirement, cost, total time available.
Decision Variable:
Ai -- hours of job A handled in shop i.
Bi -- hours of job B handled in shop i.
Ci -- hours of job C handled in shop i.
e.g. A2 -- hours of job A done in shop 2.

Objective function: minimize the total cost
Min: 89(A1+B1+C1+D1) + 81(A2+B2+C2+D2) + 84(A3+B3+C3+D3)

Constraints:
total limit on available time
A1+B1+C1+D1 <= 160
A2+B2+C2+D2 <= 160
A3+B3+C3+D3 <= 160
Explanation: the total time devoted by each shop should not exceed the limit.

There is another group of constraints, however. Since otherwise the solution found by the above formulation will be 0 !!

Another group of constraints are: Each job must be done.
A1/32 + A2/39+ A3/46 = 1
B1/151+B2/147+B3/155 = 1
C1/72 + C2/67 + C3/57 = 1
D1/118 + D2/126 + D3/121 = 1
The meaning of the constraint says that the proportion of a job done in each shop should sum up to one !

Finally, there are nonnegative constraints.
A1, A2, A3 , A4 >= 0
B1, B2, B3, B4 >= 0
C1, C2, C3, C4 >= 0
D1, D2, D3, D4 >= 0

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