Anderson medical clinic purchases a large number of cases (units) of floor polis
ID: 335143 • Letter: A
Question
Anderson medical clinic purchases a large number of cases (units) of floor polish for its own use each year from a vendor. If annual demand is 120 units, orderinq costs are $20 per order, and the annual holdinq cost rate is 25%, If there were no discount at all (unit cost $30/unit) (Refer to the Anderson clinic question above and answer) Assume that the g quantity discount schedule is available from the vendor for the polish: Order Size Discount(%) Unit Cost 0 to 49 0 $30 50 to 99 5 $28.50 100 or more 10 $27 If the discount schedule is available as specified above, the optimal purchase quantity (per order) should be a. 10 b. 15.3 C. 25.3 d. 25.96 e. 100Explanation / Answer
Solution-
In order to calculate, optimal purchase quantity based on discount schedule, we have to calculate EOQ at different unit cost and "Total cost" for each EOQ.
Given Data,
D, Annual Demand = 120 Units
Ordering Cost, K = $ 20 per order
holding cost, h = 25% * Unit Cost
Let us calculate EOQ for different holding cost based on different unit cost-
1. Order Size, 0 to 49-
h = 0.25*30 = $7.5
EOQ = sqrt(2*D*K/h) = sqrt(2*120*20/7.5) = 25.3
Total cost =P*D+K(D/EOQ)+h(EOQ/2)} = 30*120 + 20*(120/25.3) + 7.5 * 25.3/2 = 3789.7
2. Order size 50 to 99-
h = 0.25 * 28.50 = 7.125
EOQ = sqrt(2*120*20/7.125) = 25.95
Since this is not more than 50, this EOQ is not applicable.
3. Order size 100 or more-
h = 0.25 * 27 = 6.75
EOQ = sqrt(2*120*20/6.75) = 26.67
Since this is not more than 100, this EOQ is not applicable.
However, In case EOQ comes out to be not in range of discount lots, as it happened above with 50 to 99 and 100 or more, then we calculate total cost for the starting number. that is total cost for Q = 50 and Q = 100 would be calculated and then compared with total cost for Q = 25.3. which is 3789.7
Total cost for EOQ = 50 comes out to be 28.5*120 + 20*(120/50) + 7.125 * 50/2 = 3646.125
Total cost for EOQ = 100,comes out to be 27*120 + 20*(120/100) + 6.75 * 100/2 = 3601.5
Since total cost for EOQ = 100 is the lowest, 100 is the final answer.
Therefore EOQ is 100