Question

A produce distributor uses 783 packing crates a month, which it purchases at a cost of $11 each. The manager has assigned an annual carrying cost of 32 percent of the purchase price per crate. Ordering costs are $31. Currently the manager orders once a month.How much could the firm save annually in ordering and carrying costs by using the EOQ? (Round intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)

Answer 1

The firm could save approximately 663.13 in ordering and carrying costs annually by using the EOQ (Economic Order Quantity) method.

Step-by-step explanation:

1. Calculate the EOQ:

Annual demand (D) = 783 crates/month * 12 months = 9396 crates

Ordering cost (C_o) = $31

Holding cost per unit (C_h) = 32% * $11/crate = $3.52/crate

Use the EOQ formula: EOQ = √(2 * D * C_o / C_h)

EOQ ≈ √(2 * 9396 * $31 / $3.52) ≈ 407 crates

2. Calculate cost savings:

Ordering cost savings: (Current order quantity / EOQ) * Ordering cost - (Annual demand / EOQ) * Ordering cost

= (783 / 407) * $31 - (9396 / 407) * $31 ≈ $2993.88

Holding cost savings: (Current order quantity - EOQ) / 2 * Holding cost per unit

= (783 - 407) / 2 * $3.52 ≈ $661.78

3. Total cost savings:

Ordering cost savings + Holding cost savings ≈ $2993.88 + $661.78 ≈ 663.13

Therefore, the firm could achieve significant cost savings by switching to the EOQ ordering strategy.

Answer 2

Annual Savings will be ;

Ordering Cost = $2,993.88

Holding Cost = $661.78

Step-by-step explanation:

First Calculate the Economic Order Quantity (EOQ)

EOQ = √ 2 × Annual Demand × Ordering Cost per Order / Holding Cost per unit

= √ ((2 × 783× 12 × $31) / ($11 × 32%))

= 407

Note : Currently the firm orders at 783 crates per month

Savings in Ordering Cost will be :

Savings = Ordering Cost at Current Quantity - Ordering Cost at EOQ

= (Total Demand / Current Quantity × Ordering Costs) - (Total Demand / Current Quantity × Ordering Costs)

= (9396/783 × $31) - (9396/407 × $31)

= $2,993.88

Savings in Holding Cost will be :

Savings = (Current Quantity - Economic Order Quantity) / 2 × Holding Cost per unit

= (783 - 407) / 2 × ($11 × 32%)

= $661.78