Question 2 Consider the extension of EOQ which allowed for backorders. As an additional parameter to the lot-size, Q, we solve for b, where b is defined as the maximum number of backorders allowed. We also define p as the cost of backorders/unit/unit time. With the purchase cost per year being equal to a constant, we exclude that from the objective function. a) Formulate the problem by writing the average total costs (see lecture notes) b) One can take the partial derivative of the average total cost function with respect to Q and b; equate these derivatives to 0 (first-order conditions for optimality; obtain two equations to solve for unknowns and obtain the following result, (as given in the lecture notes) b*={h/(p+h)}Q* and Q*={(2KWh)*[(p+h)/h]}12 Using these results, plug those into the average total cost function you have formulated in Part a) and show that it is always less than the average total cost function obtained by EOQ with no backorders Recall: Average Total Cost (EOQ with no backorders) = {2K2h}12 Question 2 Consider the extension of EOQ which allowed for backorders. As an additional parameter to the lot-size, Q, we solve for b, where b is defined as the maximum number of backorders allowed. We also define p as the cost of backorders/unit/unit time. With the purchase cost per year being equal to a constant, we exclude that from the objective function. a) Formulate the problem by writing the average total costs (see lecture notes) b) One can take the partial derivative of the average total cost function with respect to Q and b; equate these derivatives to 0 (first-order conditions for optimality; obtain two equations to solve for unknowns and obtain the following result, (as given in the lecture notes) b*={h/(p+h)}Q* and Q*={(2KWh)*[(p+h)/h]}12 Using these results, plug those into the average total cost function you have formulated in Part a) and show that it is always less than the average total cost function obtained by EOQ with no backorders Recall: Average Total Cost (EOQ with no backorders) = {2K2h}12