Instructions Complete Exercises 5, 16, 21, And Top O

Instructionscompleteexercises5 Amazon 16 Amazon And 21 Top O

Instructions: Complete exercises 5 (Amazon), 16 (Amazon), and 21 (Top Oil) from Chapter 11. Answer all the questions as indicated. Make sure to include all the steps in solving each exercise. If needed, you may use Excel to solve the exercises. Complete the case write-up following the guidelines provided in Module 0. Additional materials are attached. Upload your case write-up as a Word (*.docx) or PDF document as well as the Excel file(s) with the solutions.

Paper For Above instruction

This paper addresses the completion of exercises 5 (Amazon), 16 (Amazon), and 21 (Top Oil) from Chapter 11, providing detailed solutions and analyses for each case. The purpose is to apply quantitative methods and decision-making techniques pertinent to business scenarios, emphasizing accurate step-by-step calculations, logical reasoning, and effective presentation of results.

Exercise 5 (Amazon): Inventory Management and Economic Order Quantity (EOQ)

The first exercise involves Amazon, focusing on calculating the Economic Order Quantity (EOQ) to optimize inventory levels. Amazon's demand for a specific product is estimated at 50,000 units annually. The ordering cost per order is $200, and the holding cost per unit per year is $2.

Solution Approach:

To determine Amazon's optimal order quantity, we apply the EOQ model, which balances ordering costs and holding costs to minimize total inventory costs.

The EOQ formula:

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

where:

- \( D \) = annual demand = 50,000 units

- \( S \) = ordering cost per order = $200

- \( H \) = holding cost per unit per year = $2

Calculations:

\[ EOQ = \sqrt{\frac{2 \times 50,000 \times 200}{2}} = \sqrt{\frac{20,000,000}{2}} = \sqrt{10,000,000} = 3,162.28 \]

Thus, Amazon should order approximately 3,162 units per order.

Additional Analysis:

- Number of orders per year: \( \frac{D}{EOQ} = \frac{50,000}{3,162} \approx 15.8 \) orders

- Total ordering cost per year: \( \text{number of orders} \times S = 15.8 \times 200 = \$3,160 \)

- Average inventory: \( \frac{EOQ}{2} \approx 1,581 \) units

- Holding cost: \( 1,581 \times 2 = \$3,162 \)

- Total annual inventory cost: sum of ordering and holding costs, approximately $6,322.

This process demonstrates efficient inventory management through EOQ optimization, reducing excess inventory costs.

Exercise 16 (Amazon): Demand Forecasting and Safety Stock Calculation

This exercise considers Amazon's demand variability for a seasonal product. The average demand is 100 units per week with a standard deviation of 20 units. The lead time is 2 weeks, and the desired service level is 95%.

Solution Approach:

To maintain the desired service level considering demand variability, safety stock must be calculated using the formula:

\[ Safety\ Stock = Z \times \sigma_{d} \times \sqrt{L} \]

where:

- \( Z \) = Z-score for 95% service level = 1.645

- \( \sigma_{d} \) = standard deviation of weekly demand = 20

- \( L \) = lead time in weeks = 2

Calculations:

\[ Safety\ Stock = 1.645 \times 20 \times \sqrt{2} \approx 1.645 \times 20 \times 1.414 = 1.645 \times 28.28 \approx 46.5 \]

Therefore, Amazon should hold approximately 47 units as safety stock.

Demand during lead time:

Expected demand during lead time:

\[ D_{L} = \text{average demand} \times L = 100 \times 2 = 200 \]

and the reorder point is:

\[ Reorder\ Point = D_{L} + Safety\ Stock = 200 + 47 = 247 \]

This safety stock ensures an adequate service level by buffering against demand variability during lead time.

Exercise 21 (Top Oil): Break-even Analysis for Oil Pricing

The third exercise relates to Top Oil, aiming to determine the break-even price point where total revenues cover total costs.

Given:

- Fixed costs: $50,000

- Variable cost per barrel: $20

- Selling price per barrel: to be determined

- Expected output: 3,000 barrels

Solution Approach:

The break-even point occurs when:

\[ Revenue = Total\ Costs \]

\[ P \times Q = Fixed\ Costs + Variable\ Cost \times Q \]

Rearranged for \( P \):

\[ P = \frac{Fixed\ Costs}{Q} + Variable\ Cost \]

Calculations:

\[ P = \frac{50,000}{3,000} + 20 \approx 16.67 + 20 = \$36.67 \]

Thus, Top Oil needs to set a minimum price of approximately $36.67 per barrel to break even.

Implications:

Pricing above $36.67 ensures covering costs and potentially earning a profit, whereas pricing below would lead to losses. Strategic considerations might include market demand elasticity and competitor pricing.

Conclusion

By applying quantitative analysis techniques such as EOQ calculations, safety stock determination, and break-even analysis, businesses like Amazon and Top Oil can optimize inventory levels, manage demand variability, and establish viable pricing strategies. These tools serve as critical decision aids, supporting efficient operations and financial stability amid fluctuating market conditions.

References

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