Use linear programming to answer the question

(Extra credit, 20 points) A company must meet demands (di, d2, ..., dn) in the next N months (that is, in month 1, the company must provide d units, month 2 must provide d, units, ..., month N must provide dy units). In month i, the company can produce r; > 0 units of product with a cost Ki +G1;. The product can be held in the inventory at the cost of w per unit per month. Here di, C, K, w are parameters known. The objective is to find a way to produce the products that satisfies the demands with minimum cost. We want to solve this problem using dynamic programming. Let f(k) be the optimal cost of satisfying the demand of (d1, d2, ..., dk) and we want to find f(N). (a) What is the value of f(1)? (That is, the minimum cost to satisfy the first week's demand, di) (b) What is the value of f(2)? (That is, the minimum cost to satisfy the first two weeks' demand) (Hint: we can either produce all two weeks' demands in the first week and then hold week 2's demand in the inventory or in each week we only produce current week's demand.) (c) Write f(k+1) in terms of f(1), f(2),..., f(k)