please formulate and solve this question as dynamic programming ( this is an operation research problem)

2. A company is planning their buying policy for a 7-month period. It manufactures crankcases for a large auto manufacturer and buys its raw material in lot sizes of 500, 700, 900, 1200, and 1500 lbs. The quantity discount prices are $3000, $4000, $5000, $6200, $7500, respectively. Anticipated usage over the 7-month period is (700, 1100, 800, 400, 900, 1200, 600) Ibs. Inventory holding cost of $0.5 per pound is incurred per month, based on the end-of-month inventory. The storage space is limited to 600 lbs. at the end of any month. There is no raw material in storage at the start and the end of the planning period. Formulate and solve this problem as dynamic programming to minimize the total cost. near a decision is made as to how many to