2. Your company sells a product whose demands over the next four months are 100, 140, 210 and 180 units, respectively. You can stock just enough supply to meet the demand each month, or you can overstock to meet the demand for two or more consecutive months. In the latter case, a holding cost of $1.2 is charged per overstocked unit per month. You estimate the unit purchase prices for the next 4 months are $15, $12, $10 and $14, respectively. A set-up cost of $200 is incurred each time a purchase order is placed. For example, if your company wants to purchase enough products for next two months at the beginning of the first month, it needs to pay $200+ $15 (100+140) + $1.2* 140 = $3968; if your company wants to purchase enough products for next three months at the beginning of the first month, then it needs to pay $200 + $15 * (100 + 140 +210) + $1.2 * 140 + $1.2 210 * 2 = $7622. Your company wants to develop a purchasing plan that will minimize the total costs of ordering, purchasing and holding an item in stock. (a) Find the optimal solution by Dijkstra's algorithm. Write down the steps clearly. (b) Find the optimal solution by Dynamic Programming (with backward recursion). Write down the steps clearly.