The Awesome Party Hat company has the following price function for its decorative balloon party hats. For orders of

The Awesome Party Hat company has the following price function for its decorative balloon party hats. For orders of less than 400 hats, the company charges 80 cents per hat; for orders of 400 or more but fewer than 900 hats, it charges 65 cents per hat; and for orders of more than 900 hats it charges 50 cents per hat. In this case the breakpoints occur at 400 and 900 hats. The discount schedule is all units because the discounted price is applied to all of the hats in the order. There is a high school debating what size standing order to place with Awesome Party Hat, and this high school uses balloon party hats at a fairly constant rate of 700 hats per year. The school district accountant estimates that the fixed cost of placing an order is $6, and the holding costs are based on a 15 % annual interest rate. Find the optimal order size for the high school and the resulting annual total cost. Assume that the value of the product is equal to the variable cost of the order.

(b) Suppose that Awesome Party Hat company has a different price function. This alternate price structure is as follows: the hats cost 80 cents each for quantites less than 400; when the order is between 400 and 900 hats the first 400 cost 80 cents each and each of the remaining hats costs 65 cents; for quantities over 900 the first 400 cost 80 cents each, the next 500 cost 65 cents each, and the remaining hats cost 50 cents each. Assume same order cost and inventory holding cost structure as part (a) , and find the optimal order size for the company and the resulting annual total cost. Compare the order size and total annual cost with part (a).

Use the simplifying assumption that the holding cost is based on the variable cost component of the per unit cost – ex: for the bracket 400 ≤ Q ≤ 900, the holding cost will be based on a per unit cost of $0.65.

Expert Answer

 Citation: Book on “Production and Operations Management” ISBN: 9788120345553…. chapters on Cost Analysis, Economic Analysis, Inventory Models, Prentice Hall Publications – Author: Dr. Panneer Selvam;

Inventory Model terms and variable assumptions:


sqrt = square root

D = Demand

O = Order Cost

C = Carrying cost = inventory holding cost

EOQ = Economic Order Quantity

VC = Variable Cost

FC = Fixed Cost

TPC = Total Product Cost

TOC = Total Ordering Cost

TCC = Total Carrying Cost

TC = Total Cost = VC + FC + TPC + TOC + TCC

VC = Number of units * Cost per unit

= 700 * 0.65 = $455

FC = whatever cost given in the question = $6 per order

Economic Order Quantity (EOQ) = sqrt (2 * D * O / C )

D = 700 hats per year

O = $6

C = 0.15 * interest rate = 0.65

EOQ = sqrt (2 * 700 * 6 / 0.65 ) = 114 hats per order


TPC = demand * purchase price (pp)

= 700 hats per year * pp = 700 * 0.65 = 455

pp will be determined based on the EOQ.

pp = variable cost of the order


TOC = Number of Orders per year * Ordering cost per order

Number of orders = D / EOQ = 700 / 114 = 6.14

Around 6 orders per annum

TOC = 6.14 * 6 = $36.9


TCC = EOQ * C = 114 * 0.65 = $74.1


= 455 + 455 + 36.9 + 74.1 = $1021

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