Question

Sunbright Citrus Products produces orange juice, grapefruit juice, and other citrus-related items. Sunbright obtains fruit concentrate from a cooperative in Orlando consisting of approximately 50 citrus growers. The cooperative will sell a minimum of 100 cans of fruit concentrate to citrus processors such as Sunbright. The cost per can is $9.90.

Last year, the cooperative developed the Incentive Bonus Program to give an incentive to their large customers to buy in quantity. It works like this: if 200 cans of concentrate are purchased, 10 cans of free concentrate are included in the deal. At 300 cans of concentrate, the cooperative will give away 30 free cans. When the quantity goes up to 400 cans of concentrate, 40 cans of concentrate will be given away free with the order.

Sunbright estimates that its annual demand for fruit concentrate is 1,000 cans. In addition, the ordering cost is estimated to be $10, while the carrying cost is estimated to be 10%, or about $1 per unit. The firm is intrigued with the Incentive Bonus Program.

My professor listed the answer as 300 units. If someone could figure out how to get what he's looking for that'd be great.

Answer 1

This is a typical quantity discount problem. It is complicated, however, by the fact that there are drawings for computers and trips, which must be considered as part of the quantity discount. When this is done, a quantity discount table can be developed and used to determine the best inventory policy. The quantity discount table is shown below.

			Average Discount
Discount	Discount	Discount	Discount Cost
1	100-199	0	$9.90
2	200-299	10 cans	9.39
3	300-399	30 cans	8.90
4	400-499	40 cans	8.89

Here is how the quantity discount table was determined. Discount 1 represents a quantity ranging from 100 to 199 units. There is no discount, and therefore the cost is simply $9.90. For discount number two, 10 free cans of product are offered. This has a total value of $99. In addition, it is possible to receive a personal computer valued at $3,000. Since there are 1,000 companies that are eligible, the expected monetary value for the personal computer drawing is $3 (3 = 3,000/1,000). This represents a total discount of $102. For 200 cans of product, this represents a 51-cent discount (0.51 = 102/200). Therefore, the discount price is $9.39. The same type of computations can be made for discount number three. The 30 cans of free product have a value of $297, and the personal computer drawing has an expected value of $3. The total discount is $300 or $1 per unit. Therefore, the average discount price is $8.90. For discount number four, there is also a drawing for a free trip. This trip has a value of $5,000 and 800 businesses are eligible for the drawing. This represents a $6.25 value ($6.25 = $5,000/800). Adding this to the $396 value for the 40 free cans and the $3 expected monetary value for the personal computer drawing, the total discount is approximately $405. The average discount therefore is $1.01. This represents a discount cost of $8.89. This information, along with the standard information for inventory control, can be used with our inventory control program to compute a quantity discount. The computer output from this program reveals that the optimal strategy is to order 300 units at a total cost of $9,083.