Question

A company orders and uses 12,150 box of pencils each year. each order has a fixed shipping cost of $150 and an additional cost of $3 per box of pencils. to store a box for a full year costs $2. what is the optimal number of orders the company should make each year

Answer 1

To minimize costs, the company should place approximately 6 orders per year, calculated using the Economic Order Quantity (EOQ) formula and rounding the result to the nearest whole number.

Step-by-step explanation:

To find the optimal number of orders a company should make to minimize costs, we use the Economic Order Quantity (EOQ) model. The yearly demand is 12,150 boxes, and each order incurs a fixed cost of $150 and a variable cost of $3 per box. There is also an annual storage cost of $2 per box.

The EOQ formula is sqrt((2DS)/H), where D is the demand, S is the fixed shipping cost per order, and H is the holding cost (storage cost) per box per year.

By substituting the given values:
D = 12,150 boxes/year
S = $150/order
H = $2/box/year
The calculation is EOQ = sqrt((2 * 12,150 * 150)/2), which simplifies to sqrt((2 * 12,150 * 150)/2) = sqrt(3,645,000), resulting in an EOQ of approximately 1910 boxes per order.

The number of orders needed per year is then found by dividing the annual demand by the EOQ: Total Orders per Year = D/EOQ = 12,150/1910, which is approximately 6.36 orders per year. Since you can't place a fraction of an order, the company should round this number to the nearest whole number, which is 6 orders per year.