Modern kitchens produces cupboards and wants to determine an optimal production schedule over 5 days. Each day has demand, di, a production cost per unit, Si, a storage cost between period i - 1 and i, ti, and a fixed cost for producing in each time period, ci,. No cupboards are on stock neither initially nor at the end of the final period. Some data is given below:
t 1 2 3 4 5
Si 3 3 4 5 5
ti 0 1 1 1 2
ci 30 30 30 30 30
di 32 41 48 36 20
Determine the optimal production plan, i.e. , how many cupboards to produce each day in order to minimize the total production cost.