Wang Distribution has an annual demand for an airport metal detector of 1,420 units. The cost of a typical detector to Wang is $400. Carrying cost is estimated to be 19% of the unit cost, and the orde

The EOQ without the discount is 178 units. To calculate the EOQ, we can use the following formula: EOQ = ?[(2SD)/H] Where: S = Annual demand = 1,420 units D = Ordering cost = $24 H = Carrying cost as a percentage of unit cost = 0.19 x $400 = $76 Plugging in the values, we get: EOQ = ?[(2 x 1,420 x 24)/76] = 177.79 Rounding up to the nearest whole unit, the EOQ without the discount is 178 units. Now, let's consider whether Wang should take the quantity discount. Ordering in quantities of 300 or more would result in a cost savings of 4% per unit, or $16 per unit. However, the increase in the order quantity would also lead to an increase in carrying cost. To calculate the total cost of ordering with the discount, we can use the following formula: Total cost = (S/Q) x (D + (Q/2)H) + Q x P Where: Q = Order quantity P = Cost per unit after discount = $400 - $16 = $384 Let's try calculating the total cost for an order quantity of 300: Total cost = (1420/300) x (24 + (300/2) x 76) + 300 x 384 Total cost = $2,874.67 Now, let's calculate the total cost for an order quantity of 178 (the EOQ without the discount): Total cost = (1420/178) x (24 + (178/2) x 76) + 178 x 400 Total cost = $2,869.34 As we can see, ordering the EOQ without the discount results in a slightly lower total cost than ordering in quantities of 300 or more with the discount. Therefore, Wang should not take the quantity discount and instead order the EOQ without the discount, which is 178 units.