What is the maximum allowable scrap rate for Process A to ensure a raw material input of 18,519 or less?

To determine the maximum allowable scrap rate for Process A that ensures a raw material input of 18,519 or less, it's important to understand the relationship between the scrap rate and the total input of raw materials.

The scrap rate refers to the percentage of the material that is wasted or not used in the end product. When there is a higher scrap rate, more raw materials are required to produce the final output. Consequently, a lower scrap rate means that less raw material is wasted and therefore less is needed to reach the desired output.

When the scrap rate is given as a percentage, the formula to calculate the necessary input of raw materials can be expressed as follows:

[ \text{Input} = \text{Output} / (1 - \text{Scrap Rate}) ]

To determine the maximum scrap rate for a total input of 18,519, you can rearrange this equation. Assuming you want to find the scrap rate that aligns with an output while keeping the input at or below 18,519, you would set the inequality for various scrap rates:

• If the scrap rate is, for instance, 25%, the input becomes larger because only 75% of the material is utilized. Thus:

[ \