Question

1. A lab is trying to determine how many test kits it should order from its supplier. They use 780 kits per year. The annual holding cost is $3 per kit per year. The ordering cost is $15 per order. The supplier delivers their orders all at one time, but offers a quantity discount. What is the optimum condition (order quantity) and total cost (ordering, holding and item cost)? Draw the Order quantity (Q) verses Total Annual Cost graph with 3 item prices (as shown in Figure 12.7 of the textbook).

Quantity	$Price
1-72	60
73-144	56
145 and more	53

Answer 1

Given :

Annual demand =780

Annual holding cost per kit per year =3

Cost per order =15

Optimal order quantity also known as Economic order quantity is given by the formula ,

EOQ=sqrt(2*Annual demand*cost per order/holding cost per unit per year)

=sqrt(2*780*15/3)

=88.317

=88

Number of orders =Annual demand/EOQ=780/88 =8.86 =9 orders per year

Total cost=ordering cost+holding cost+purchasing cost

=No of orders * cost per order+average inventory *inventory holding cost +Annual demand * Purchase price

=9*15+88/2* 3+780*56

=$ 43947

Order quantity versus Total cost graph

Calculations are as shown below :