Question

A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50 tons per day. Setup costs $100, and storage and handling costs are $5 per ton a year. The firm operates 200 days a year. (Note: 1 ton = 2,000 pounds.)

a. How many bags per run are optimal? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
b. What would the average inventory be for this lot size? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
c. Determine the approximate length of a production run, in days. (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
d. About how many runs per year would there be? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)

Answer 1

The optimal number of bags per run for the chemical firm is 64.

Step-by-step explanation:

To determine the number of bags per run that is optimal,we need to calculate the economic order quantity (EOQ). EOQ can be calculated using the formula: EOQ = sqrt((2 x Demand x Setup Cost) / (Storage and Handling Cost x Production Capacity)). Plugging in the given values, EOQ = sqrt((2 x 20 x 200 x 100) / (5 x 50 x 1000)). Simplifying this, EOQ = sqrt(4000), which is approximately 63.24.

Since we cannot have fractional bags, we round this value up to the nearest whole number, which is 64. Therefore, the optimal number of bags per run is 64.