Question

A bakery buys sugar from a big distributor to use in baking cakes. Typically, they use 3673 bags of sugar in a year. The price of sugar is typically $11 per bag. The cost to the bakery for placing an order is $29, and the annual carrying cost is $18 per bag. The distributor has offered the bakery the following volume discount schedule:

Order Size	Discount rate on the original price
1--449	0 percent
450--799	5 percent
more than 800	10 percent

We are trying to find how many bags of sugar should the store order, whenever they place a new order of sugar. Assume 364 days a year and 52 weeks a year.
IMPORTANT: Note, the discounts off of original price are reported. You need to calculate the actual prices.
Keep two decimal places in your calculations (Example: 141.55). If we ignore the discounts, how many bags of sugar should we order? (Example: 141.55)
Fill in the blanks:

Orde Quantity	Unit Price to Pay	Total Annual Inventory Related Cost
Quantity from EOQ model
Enough to get 5 percent discount
Enough to get 10 percent discount

Based on this quantity discount information, how may bags of sugar should the store order? (Example: 141.55)
How often (in "days") should the bakery order? (Example: 13.22)

Answer 1

Annual demand = 3673 = D
EOQ = Square root ((2*D*S)/h) S = ordering cost per order = $29 and h = holding cost = $18

EOQ = Sqrt((2*3673*29)/18) = 108.7898075 = 108.79 (Rounded to 2 decimal places)

Total Annual cost = Annual ordering cost + Annual inventory holding cost + purchase cost

= (3673/108.79)*29 + (108.79/2)*18 + 3673*11
= 42361.21654 = 42361.22 (Rounded to 2 decimal places)

To avail 5% discount ordering quantity needs to be minimum 450

Total Annual cost = Annual ordering cost + Annual inventory holding cost + purchase cost

= (3673/450)*29 + (450/2)*18 + 3673*11*0.95

= 42669.55444 = 42669.55 (Rounded to 2 decimal places)

To avail 10% discount ordering quantity needs to be minimum 800

Total Annual cost = Annual ordering cost + Annual inventory holding cost + purchase cost

= (3673/800)*29 + (800/2)*18 + 3673*11*0.9
= 43695.84625 = 43695.85 (Rounded to 2 decimal places)

No of bags to order 108.79 as it has minimum total annual cost (Ans)

If we ignore the discounts, No of bags to order = 108.79 (Ans)

Orde Quantity	Unit Price to Pay	Total Annual Inventory Related Cost
Quantity from EOQ model	11	42361.22
Enough to get 5 percent discount	10.45	42669.55
Enough to get 10 percent discount	9.9	43695.85

Based on this quantity discount information, how may bags of sugar should the store order?

Ans: 108.79

How often (in "days") should the bakery order?

Ans: No of orders in a year = 3673/108.79 = 33.76

Days between orders = 364/33.76 = 10.78199052 = 10.78 (Rounded to 2 decimal places)