Question

A manufacturer of hospital supplies has a uniform annual demand for 80,000 boxes of bandages. It costs ​$20 to store one box of bandages for one year and $320 to set up the plant for production. How many times a year should the company produce boxes of bandages in order to minimize the total storage and setup​ costs?

Answer 1

To minimize total storage and setup costs, the company should calculate the Economic Order Quantity (EOQ). With an annual demand of 80,000 boxes, setup cost of $320, and holding cost of $20 per box per year, the EOQ formula yields an optimal production run size of 1,600 boxes. Consequently, the company should produce bandages 50 times per year.

Step-by-step explanation:

The student's question involves finding the optimal number of production runs to minimize the total storage and setup costs for a company manufacturing boxes of bandages. This is a classic problem in inventory management and can be solved using the Economic Order Quantity (EOQ) model.

The EOQ model determines the optimal order quantity that minimizes the total holding costs and ordering costs. The EOQ formula is given by the square root of (2DS/H), where D represents the annual demand, S is the setup cost or ordering cost, and H is the holding or storage cost per unit per year.

For the given problem:

• Annual demand (D) = 80,000 boxes
• Setup cost (S) = $320
• Holding cost (H) = $20 per box per year

Plugging these values into the EOQ formula:

EOQ = √((2 * 80,000 * 320) / 20)

EOQ = √(51,200,000 / 20)

EOQ = √2,560,000

EOQ = 1,600 boxes

This means the optimal production run size is 1,600 boxes of bandages. To determine the number of times the company should produce bandages per year, we divide the annual demand by the EOQ:

Number of production runs per year = D / EOQ

Number of production runs per year = 80,000 / 1,600

Number of production runs per year = 50 times

Therefore, the company should produce bandages 50 times a year to minimize the total storage and setup costs.