Question

b. now assume that six percent of the chemical is not used and disposed of, with a disposal cost of $0.50/lb. find the eoq and total cost when disposal costs are incorporated into the model. (hint: add to the holding cost the disposal cost times the percent of product that is disposed of.) round your answer for the eoq to the nearest whole number and round your answer for the total cost to the nearest cent. use the rounded eoq value in your calculations. do not round any other intermediate calculations.
economic order quantity: lb
total cost: $

c. what implications do these results have for sustainability practices?

although the total cost in part b is -select- , by adjusting the economic order quantity, the company -select- actually save additional costs while protecting the environment.

Explanation:

To solve this, we likely need the basic EOQ formula and the holding cost details (which are missing here, but let's assume we have annual demand \( D \), ordering cost \( S \), and original holding cost per unit \( H \)). Let's denote:

Part b:

Step 1: Adjust Holding Cost

Let the original holding cost per unit be \( H \), disposal cost per lb is \( \$0.50 \), and 6% is disposed. So new holding cost \( H' = H + 0.06 \times 0.50 \).

Step 2: EOQ Formula

The EOQ formula is \( EOQ = \sqrt{\frac{2DS}{H'}} \). We need \( D \), \( S \), and \( H \) (or \( H' \)) to compute. Suppose (for example, if we had \( D = 10000 \) lb/year, \( S = \$50 \), \( H = \$2 \)):

• \( H' = 2 + 0.06 \times 0.50 = 2 + 0.03 = 2.03 \)
• \( EOQ = \sqrt{\frac{2 \times 10000 \times 50}{2.03}} = \sqrt{\frac{1000000}{2.03}} \approx \sqrt{492610.84} \approx 702 \) (rounded)

Step 3: Total Cost (TC)

\( TC = \frac{D}{EOQ} \times S + \frac{EOQ}{2} \times H' \)
Using \( EOQ = 702 \), \( D = 10000 \), \( S = 50 \), \( H' = 2.03 \):

• Ordering cost: \( \frac{10000}{702} \times 50 \approx 14.245 \times 50 \approx 712.25 \)
• Holding cost: \( \frac{702}{2} \times 2.03 \approx 351 \times 2.03 \approx 712.53 \)
• Total cost: \( 712.25 + 712.53 \approx 1424.78 \)

Part c:

If total cost in part b is (say) higher than part a (without disposal), but by adjusting EOQ, the company can actually save additional costs while protecting the environment (since reducing waste/disposal aligns with sustainability). So:

• First select: "higher" (if TC increases due to disposal cost inclusion)
• Second select: "can"

Note:

Since the original problem's data (like \( D \), \( S \), \( H \)) is missing, the above is a hypothetical example. For the actual problem, plug in the given values for \( D \) (annual demand), \( S \) (ordering cost per order), and original \( H \) (holding cost per unit per year) to compute \( H' \), then EOQ and TC.

Final Answers (Hypothetical Example):

• EOQ: \( \boldsymbol{702} \) lb (varies with actual data)
• Total cost: \( \boldsymbol{\$1424.78} \) (varies with actual data)
• Part c: First select "higher", Second select "can"

Answer:

To solve this, we likely need the basic EOQ formula and the holding cost details (which are missing here, but let's assume we have annual demand \( D \), ordering cost \( S \), and original holding cost per unit \( H \)). Let's denote:

Part b:

Step 1: Adjust Holding Cost

Let the original holding cost per unit be \( H \), disposal cost per lb is \( \$0.50 \), and 6% is disposed. So new holding cost \( H' = H + 0.06 \times 0.50 \).

Step 2: EOQ Formula

The EOQ formula is \( EOQ = \sqrt{\frac{2DS}{H'}} \). We need \( D \), \( S \), and \( H \) (or \( H' \)) to compute. Suppose (for example, if we had \( D = 10000 \) lb/year, \( S = \$50 \), \( H = \$2 \)):

• \( H' = 2 + 0.06 \times 0.50 = 2 + 0.03 = 2.03 \)
• \( EOQ = \sqrt{\frac{2 \times 10000 \times 50}{2.03}} = \sqrt{\frac{1000000}{2.03}} \approx \sqrt{492610.84} \approx 702 \) (rounded)

Step 3: Total Cost (TC)

\( TC = \frac{D}{EOQ} \times S + \frac{EOQ}{2} \times H' \)
Using \( EOQ = 702 \), \( D = 10000 \), \( S = 50 \), \( H' = 2.03 \):

• Ordering cost: \( \frac{10000}{702} \times 50 \approx 14.245 \times 50 \approx 712.25 \)
• Holding cost: \( \frac{702}{2} \times 2.03 \approx 351 \times 2.03 \approx 712.53 \)
• Total cost: \( 712.25 + 712.53 \approx 1424.78 \)

Part c:

If total cost in part b is (say) higher than part a (without disposal), but by adjusting EOQ, the company can actually save additional costs while protecting the environment (since reducing waste/disposal aligns with sustainability). So:

• First select: "higher" (if TC increases due to disposal cost inclusion)
• Second select: "can"

Note:

Since the original problem's data (like \( D \), \( S \), \( H \)) is missing, the above is a hypothetical example. For the actual problem, plug in the given values for \( D \) (annual demand), \( S \) (ordering cost per order), and original \( H \) (holding cost per unit per year) to compute \( H' \), then EOQ and TC.

Final Answers (Hypothetical Example):

• EOQ: \( \boldsymbol{702} \) lb (varies with actual data)
• Total cost: \( \boldsymbol{\$1424.78} \) (varies with actual data)
• Part c: First select "higher", Second select "can"