A feed dealer buys corn from grain farmers and distributes and sells it to livestock farmers. In this exercise, the stages in the DP problem coincide with periods of times, specifically three months: January, February, and March. At the beginning of each month, the dealer must purchase enough corn to satisfy the feed demand of its customers. Assume the following data has been gathered for this exercise:
|
Month
|
Demand (million lbs)
|
Cost per million bushels of corn ($ million)
|
Storage cost per million bushels ($ million)
|
|
January
|
1
|
4.00
|
0.15
|
|
February
|
3
|
4.15
|
0.15
|
|
March
|
2
|
4.25
|
0.15
|
Assume no inventories are desired at the end of March, and there are no beginning inventories in January. Solve this exercise using DP to minimize total purchase plus storage costs.