Questions: Douglas Boats is a supplier of boating equipment for the states of Oregon and Washington. It sells 5,000 White Marine WM-4 diesel engines every year. These engines are shipped to Douglas in a shipping container of 100 cubic feet, and Douglas Boats keeps the warehouse full of these WM-4 engines. The warehouse can hold 5,000 cubic feet of boating supplies. Douglas estimates that the ordering cost is 10 per order, and the carrying cost is estimated to be 10 per engine per year. Douglas Boats is considering the possibility of expanding the warehouse for the WM-4 engines. Assume demand is constant throughout the year.

Solution Steps

To determine if Douglas Boats should expand the warehouse, we need to calculate the total cost of ordering and carrying the engines in both the current and expanded warehouse scenarios. We will then compare these costs to see if the expansion is worth it.

1. Calculate the Economic Order Quantity (EOQ) for the current warehouse capacity.
2. Calculate the total cost (ordering cost + carrying cost) for the current warehouse capacity.
3. Calculate the EOQ for the expanded warehouse capacity.
4. Calculate the total cost for the expanded warehouse capacity.
5. Compare the total costs to determine the worth of the expansion.

The Economic Order Quantity (EOQ) for the current warehouse capacity is calculated using the formula:

\[ EOQ = \sqrt{\frac{2DS}{H}} \]

where:

• \(D = 5000\) (annual demand),
• \(S = 10\) (ordering cost),
• \(H = 10\) (carrying cost).

Substituting the values, we find:

\[ EOQ_{current} = \sqrt{\frac{2 \times 5000 \times 10}{10}} = 100 \]

The total cost for the current warehouse is given by:

\[ Total\ Cost_{current} = \left(\frac{D}{EOQ_{current}}\right)S + \left(\frac{EOQ_{current}}{2}\right)H \]

Substituting the values:

\[ Total\ Cost_{current} = \left(\frac{5000}{100}\right) \times 10 + \left(\frac{100}{2}\right) \times 10 = 500 + 500 = 1000 \]

The EOQ for the expanded warehouse capacity is calculated using the same formula:

\[ EOQ_{expanded} = \sqrt{\frac{2DS}{H}} = 100 \]

The total cost for the expanded warehouse is:

\[ Total\ Cost_{expanded} = \left(\frac{D}{EOQ_{expanded}}\right)S + \left(\frac{EOQ_{expanded}}{2}\right)H \]

Substituting the values:

\[ Total\ Cost_{expanded} = \left(\frac{5000}{100}\right) \times 10 + \left(\frac{100}{2}\right) \times 10 = 500 + 500 = 1000 \]

The worth of the expansion is calculated as:

\[ Worth\ of\ Expansion = Total\ Cost_{current} - Total\ Cost_{expanded} = 1000 - 1000 = 0 \]

Final Answer