The economic order quantity (EOQ) refers to the ideal order quantity a company should purchase in order to minimize its inventory costs, such as holding costs, shortage costs, and order costs. EOQ is necessarily used in inventory management, which is the oversight of the ordering, storing, and use of a company's inventory. Inventory management is tasked with calculating the number of units a company should add to its inventory with each batch order to reduce the total costs of its inventory.

Question: To minimize their annual holding and order cost, a small business wants to apply the (EOQ) model to compute the optimal number of itms to add to their inventory with each order.

 

 

order cost (Ci) Itm (i) Yearly Demand (D;) price (Pi) holding cost (h) 1 200 9.5 23 30 2 1000 21.5 50 40 3 3400 11.6 90 25 The following is a list of definitions: CD Annual ordering costs per item, h-Annual holding costs per item, G - - Gi 2 Optimal No of items to add to their inventory (EOQ) and PD; - Annual purchase cost per item The total annual cost of item i is given by the function: Li (Gi) PiDi +- + Ci Dihi Gi Gi 2 And the EOQ (G) of each item is given by solving the first order differential equation i) ii) iii) dL = 0 dG Find the answer to the differential equation and as a result, the best optimal value of G for each item in the above table. The company has a yearly budget of 3050 to spend on holding costs. Formulate a constrained nonlinear optimisation problem that minimises the total cost L(G) =i Li (G) subject to the constraint that the total annual holding costs must be < 3050 Compute the Hessian(H) of the function L and show your working.