Sandwich Bags

• The production line is capable of producing 500 24-inch-wide plastic bag blanks per hour, which can be split and converted into plastic bags according to customer demand.
• The production line operates for 20 hours per day, 5 days per week, and 50 weeks per year.

ConsumerPackagingCo should prioritize producing 4-inch plastic bags first, which yield the highest profits of $60 per hour. After producing 4-inch bags, the client should focus on 8-inch plastic bags, which yield profits of $45 per hour. The 12-inch plastic bags yield the lowest profits of $40 per hour, making them the least attractive option.

Due to the limited production capacity of 5,000 hours per year, ConsumerPackagingCo should produce 4-inch plastic bags 60% of the time and 8-inch plastic bags 40% of the time.

• The costs of a new production line are $750k.
• The required payback period is 5 years.
• The market is mature, and no dramatic changes are anticipated.

While ConsumerPackagingCo would be able to meet the total demand for 12-inch plastic bags, the generated profits of $600k would be less than the investment costs of $750k, resulting in a loss of $150k after 5 years.

• Adaptability to market dynamics: Although the market is considered mature, unanticipated changes or opportunities may arise, increasing the demand for the 12-inch plastic bags or other types of bags. A new production line would allow ConsumerPackagingCo to be more responsive to market fluctuations.
• Product portfolio diversification: A new production line could allow ConsumerPackagingCo to diversify its product offerings, enabling the company to cater to different customer needs and preferences. This could lead to new revenue streams and a more robust business model.
• Flexible capacity utilization: If ConsumerPackagingCo finds that it does not require the full capacity of the new production line, the company could consider renting out the excess capacity to other businesses. This would generate additional revenue, offsetting the investment costs and improving the return on investment.

Depending on the design of the new plastic bag, ConsumerPackagingCo could choose different options to generate an additional $30k in annual profits, such as $0.02 profits per bag at 1.5m bags produced, $0.015 profits per bag at 2.0m bags produced, or $0.01 profits per bag at 3.0m bags produced.

Since this profit-volume function is linear, there are always two endpoints, namely the intersections with the x- and the y-axes. The candidate can solve the intersection points either geometrically or algebraically. The algebraic solution is shown below using the two options $0.02 profits per bag at 1.5m bags produced and $0.01 profits per bag at 3.0m bags produced.

If the two options we chose for generating an additional $30k in profits are valid, the two endpoints would be $0.03 and 4.5m, meaning ConsumerPackagingCo would not find any buyers at $0.03 or more profits per bag and would not generate any profits per bag when producing 4.5m bags or more.

• First of all, in order to maximize profits under the current production constraints, I would advise ConsumerPackagingCo to prioritize producing 4-inch plastic bags, which yield the highest profits of $60 per hour. After producing 4-inch bags, the client should focus on 8-inch plastic bags, which yield profits of $45 per hour. The 12-inch plastic bags yield the lowest profits of $40 per hour, making them the least attractive option. Due to the limited production capacity of 5,000 hours per year, ConsumerPackagingCo should produce 4-inch plastic bags 60% of the time and 8-inch plastic bags 40% of the time, resulting in annual profits of $270k.
• Regarding investing in a second production line, the generated profits of $600k from producing 12-inch plastic bags would be less than the investment costs of $750k, resulting in a loss of $150k after 5 years. However, investing in a new production line might still be meaningful, considering adaptability to market dynamics, product portfolio diversification, and flexible capacity utilization.
• If ConsumerPackagingCo were to produce a new bag, they would need to generate an additional $30k in annual profits to justify investing in a new production line. This could be achieved through different options, such as $0.02 profits per bag at 1.5 million bags produced, $0.015 profits per bag at 2.0 million bags produced, or $0.01 profits per bag at 3.0 million bags produced.
• As next steps, ConsumerPackagingCo should first implement the production optimization strategy by focusing on 4-inch and 8-inch plastic bags. Secondly, they should conduct a thorough market analysis to identify potential new plastic bags that can generate the additional profits required to justify investing in a second production line. Thirdly, assessing the potential to rent out excess capacity could help offset the investment costs of a second production line.