Question

b)The office manager for the Gotham Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6,500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company:
Order Quantity (boxes) Price per box ($)
200-999 16
1,000-2,999 14
3,000-5,999 13
6,000+ 12

Determine the optimal order quantity and the total annual inventory cost.
c)Determine the optimal order quantity and the total annual inventory cost, if the carrying cost is 20% of the price of a box of stationery.

Answer 1

Optimal oder quantity =

$$\sqrt{2×d×co\over ch}$$

Where d demand in this case its what the company uses

Co is the carrying cost

Ch is holding cost

$$\sqrt{2×6500×28\over3}$$

The optimal quantity is $\therefore$ 348.32

The total cost is therefore

Odering cost + carrying cost +holding cost +purchasing cost

$({65000\over348}×28)+{348\over 2}({6500\over28}×3)$

105044.98