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 higher , by adjusting the economic order quantity, the company can actually save additional costs while protecting the environment.

Explanation:

To solve part (b), we need the basic EOQ formula and the given data (which we assume includes annual demand \( D \), ordering cost \( S \), and holding cost per unit \( H \), though they are not provided here. Let's assume typical values for illustration (e.g., from a standard EOQ problem: \( D = 10000 \) lb/year, \( S = \$50 \) per order, \( H = \$2 \) per lb/year).

Step 1: Adjust Holding Cost

The disposal cost is \( \$0.50/\text{lb} \) and 6% of the chemical is disposed. So, the additional holding cost from disposal is \( 0.06 \times 0.50 = \$0.03/\text{lb} \).
New holding cost \( H_{\text{new}} = H + 0.03 \). For our example, \( H_{\text{new}} = 2 + 0.03 = \$2.03/\text{lb/year} \).

Step 2: Calculate EOQ

The EOQ formula is \( \text{EOQ} = \sqrt{\frac{2DS}{H_{\text{new}}}} \).
Substituting \( D = 10000 \), \( S = 50 \), \( H_{\text{new}} = 2.03 \):
\[
\text{EOQ} = \sqrt{\frac{2 \times 10000 \times 50}{2.03}} = \sqrt{\frac{1000000}{2.03}} \approx \sqrt{492610.84} \approx 702 \text{ lb (rounded)}.
\]

Step 3: Calculate Total Cost

Total cost (TC) formula: \( \text{TC} = \frac{D}{Q}S + \frac{Q}{2}H_{\text{new}} \), where \( Q = \text{EOQ} \).
Substituting \( D = 10000 \), \( S = 50 \), \( Q = 702 \), \( H_{\text{new}} = 2.03 \):
\[
\text{TC} = \frac{10000}{702} \times 50 + \frac{702}{2} \times 2.03
\]
\[
\text{TC} \approx 712.25 + 713.03 \approx \$1425.28.
\]

Note:

Since the original problem’s data ( \( D \), \( S \), \( H \)) is not provided, the above is a hypothetical example. For the actual problem, substitute the given values for \( D \), \( S \), and \( H \) into the steps.

Final Answer (Hypothetical Example):

• Economic Order Quantity: \( \boldsymbol{702} \) lb
• Total cost: \( \boldsymbol{\$1425.28} \)

(If you provide the actual \( D \), \( S \), and \( H \), we can compute the exact values.)

Answer:

To solve part (b), we need the basic EOQ formula and the given data (which we assume includes annual demand \( D \), ordering cost \( S \), and holding cost per unit \( H \), though they are not provided here. Let's assume typical values for illustration (e.g., from a standard EOQ problem: \( D = 10000 \) lb/year, \( S = \$50 \) per order, \( H = \$2 \) per lb/year).

Step 1: Adjust Holding Cost

The disposal cost is \( \$0.50/\text{lb} \) and 6% of the chemical is disposed. So, the additional holding cost from disposal is \( 0.06 \times 0.50 = \$0.03/\text{lb} \).
New holding cost \( H_{\text{new}} = H + 0.03 \). For our example, \( H_{\text{new}} = 2 + 0.03 = \$2.03/\text{lb/year} \).

Step 2: Calculate EOQ

The EOQ formula is \( \text{EOQ} = \sqrt{\frac{2DS}{H_{\text{new}}}} \).
Substituting \( D = 10000 \), \( S = 50 \), \( H_{\text{new}} = 2.03 \):
\[
\text{EOQ} = \sqrt{\frac{2 \times 10000 \times 50}{2.03}} = \sqrt{\frac{1000000}{2.03}} \approx \sqrt{492610.84} \approx 702 \text{ lb (rounded)}.
\]

Step 3: Calculate Total Cost

Total cost (TC) formula: \( \text{TC} = \frac{D}{Q}S + \frac{Q}{2}H_{\text{new}} \), where \( Q = \text{EOQ} \).
Substituting \( D = 10000 \), \( S = 50 \), \( Q = 702 \), \( H_{\text{new}} = 2.03 \):
\[
\text{TC} = \frac{10000}{702} \times 50 + \frac{702}{2} \times 2.03
\]
\[
\text{TC} \approx 712.25 + 713.03 \approx \$1425.28.
\]

Note:

Since the original problem’s data ( \( D \), \( S \), \( H \)) is not provided, the above is a hypothetical example. For the actual problem, substitute the given values for \( D \), \( S \), and \( H \) into the steps.

Final Answer (Hypothetical Example):

• Economic Order Quantity: \( \boldsymbol{702} \) lb
• Total cost: \( \boldsymbol{\$1425.28} \)

(If you provide the actual \( D \), \( S \), and \( H \), we can compute the exact values.)