Janis has demand for 40,000 desks p.a. and the purchase price of each desk is 25. There are ordering costs of 20 for each order placed. Inventory holding costs amount to 10% p.a. of inventory value. Calculate the inventory costs p.a. for the following order quantities, and plot them on a graph:

First, let's determine the annual holding cost per unit. The inventory holding cost rate is 10% p.a. of inventory value, and the purchase price is $25 per desk.

$Annual Holding Cost per unit (H) = Holding Cost Rate \times Purchase Price$ $H = 0.10 \times \$25 = \$2.50 per unit p.a.$

The total annual inventory cost (TC) is the sum of the annual ordering cost and the annual holding cost. $TC = \left(\frac{Annual Demand (D)}{Order Quantity (Q)}\right) \times Ordering Cost per Order (S) + \left(\frac{Order Quantity (Q)}{2}\right) \times Annual Holding Cost per unit (H)$ Given: Annual Demand (D) = 40,000 units Ordering Cost per Order (S) = $20 Annual Holding Cost per unit (H) =$2.50

a) 500 units Step 1: Calculate Annual Ordering Cost. $Annual Ordering Cost = \frac{40,000}{500} \times \$20 = 80 \times \$20 = \$1,600$ Step 2: Calculate Annual Holding Cost. $Annual Holding Cost = \frac{500}{2} \times \$2.50 = 250 \times \$2.50 = \$625$ Step 3: Calculate Total Annual Inventory Cost. $TC = \$1,600 + \$625 = \$2,225$

b) 750 units Step 1: Calculate Annual Ordering Cost. $Annual Ordering Cost = \frac{40,000}{750} \times \$20 \approx 53.33 \times \$20 = \$1,066.67$ Step 2: Calculate Annual Holding Cost. $Annual Holding Cost = \frac{750}{2} \times \$2.50 = 375 \times \$2.50 = \$937.50$ Step 3: Calculate Total Annual Inventory Cost. $TC = \$1,066.67 + \$937.50 = \$2,004.17$

c) 1,000 units Step 1: Calculate Annual Ordering Cost. $Annual Ordering Cost = \frac{40,000}{1,000} \times \$20 = 40 \times \$20 = \$800$ Step 2: Calculate Annual Holding Cost. $Annual Holding Cost = \frac{1,000}{2} \times \$2.50 = 500 \times \$2.50 = \$1,250$ Step 3: Calculate Total Annual Inventory Cost. $TC = \$800 + \$1,250 = \$2,050$

d) 1,250 units Step 1: Calculate Annual Ordering Cost. $Annual Ordering Cost = \frac{40,000}{1,250} \times \$20 = 32 \times \$20 = \$640$ Step 2: Calculate Annual Holding Cost. $Annual Holding Cost = \frac{1,250}{2} \times \$2.50 = 625 \times \$2.50 = \$1,562.50$ Step 3: Calculate Total Annual Inventory Cost. $TC = \$640 + \$1,562.50 = \$2,202.50$

To plot these on a graph, you would use the order quantity (Q) on the x-axis and the total annual inventory cost (TC) on the y-axis. The points to plot are: • (500 units, $2,225) • (750 units,$2,004.17) • (1,000 units, $2,050) • (1,250 units,$2,202.50)

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