A company offers its customers the following discounts, granted according to the

Question

A company offers its customers the following discounts, granted according to the order quantity; If more is requested, the discount is higher, therefore, the unit cost is lower:

In this way, we assume that the company offers the following information:

Annual demand = 800 units

Cost per unit (Cu) = $ 40

Cost of each order = $ 20

Storage cost = 15% * Cu

A. If you are a customer, what is the quantity of products you should order and what would be the total annual cost? (Explain)

B. If there is only capacity to make 65 units, what is the unit cost at which the product should be sold? (Explain)

Discount Category Quantity Discount % 090 5% 8% Category 2 3 0-999 1000-2649 2650

Explanation / Answer

A. As a customer, the quantity of products ordered should have minimum cost. Since the annual demand is 800 units and a 15% storage cost is also involved, the ordering should be of smaller amount as per requirement.

Cost/unit = $40

order cost = $20

storage cost = 15% * Cost/unit= 15%*40

So, as per above table, the customer should go for 1000 quantities where after the discount the annual cost will be lower than the category 1 - 999 quantity option. Since the annual demand is only 800 and to keep the storage cost low, 1000 will be ideal quantity to order.

For 1000 quantity, the annual cost would be $39220

unit cost = 1000*40 = $40000

order cost = $20

storage cost of 200 extra units = $200*15%*40= 1200

Discount count = 5%*40*1000 = $2000

Total annual cost = unit cost + storage cost + order cost - discount = $39220

Alternatively if a large quantity is to be ordered irrespective of the cost, then the more quantity ordered, the cost for that number of quantity can be optimized. So if category 3 is ordered ith 2650 quantity , then the annual cost of order would be $108640 while if the same thing as ordered through category 2 with 1500 quantity twice then the total annual cost would be $122440. So in that scenario category 3 would be a better option to category 2 as per below table:

B. If there is capacity to make only 65 units then the total cost would be:

unit cost = $40*65 = $2600

cost of each order = $20

Storage cost = $0 because the production is less than demand

Total cost encountered would be = $2620

To keep a no profit no loss scenario the selling price would be = $2620/65 = $40.3

if there is no immediate demand then we can add the storage cost to the annual cost = 15%*65*40 = $390

Total cost = $2620 +390= $3010

To keep a no profit no loss scenario the selling price would be = $3010/65 = $46.3

Category Quantity Discount% Quantity ordered Cost per unit Ordering cost storage cost Discount Total annual Cost 1 0-999 0% 999 39960 20 1194 0 39984 2 1000-2649 5% 1000 40000 20 1200 2000 39220 3 >=2650 8% 2650 106000 20 11100 8480 108640

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