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:

$\text{Annual Ordering Cost} = \frac{40,000}{500} \times \$20 = 80 \times \$20 = \$1,600$

$\text{Annual Holding Cost} = \frac{500}{2} \times \$2.50 = 250 \times \$2.50 = \$625$

$\text{TC} = \$1,600 + \$625 = \boxed{\$2,225}$

$\text{Annual Ordering Cost} = \frac{40,000}{750} \times \$20 \approx 53.33 \times \$20 = \$1,066.67$

$\text{Annual Holding Cost} = \frac{750}{2} \times \$2.50 = 375 \times \$2.50 = \$937.50$

$\text{TC} = \$1,066.67 + \$937.50 = \boxed{\$2,004.17}$

$\text{Annual Ordering Cost} = \frac{40,000}{1,000} \times \$20 = 40 \times \$20 = \$800$

$\text{Annual Holding Cost} = \frac{1,000}{2} \times \$2.50 = 500 \times \$2.50 = \$1,250$

$\text{TC} = \$800 + \$1,250 = \boxed{\$2,050}$

$\text{Annual Ordering Cost} = \frac{40,000}{1,250} \times \$20 = 32 \times \$20 = \$640$

$\text{Annual Holding Cost} = \frac{1,250}{2} \times \$2.50 = 625 \times \$2.50 = \$1,562.50$

$\text{TC} = \$640 + \$1,562.50 = \boxed{\$2,202.50}$

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)