Sandwich Bags

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Problem Definition

Your client is a very small consumer packaging company. One of their product lines is plastic bags that are designed to store food. They currently have one production machine dedicated to this product.

Since product demand currently exceeds your client’s production capacity, they want you to answer two key questions:

1. How can they best utilize their current bag capacity?

2. Should they invest in a new bag machine?


Since this is an interviewer-led case, the interviewer should guide through the interview.

The case is split into three parts.

In the first part, the interviewee needs to evaluate existing products and machine capacity. The interviewee should calculate the client’s most profitable product mix, keeping production capacity in mind.

The second part is directed towards answering the second key question of investment in a new bag machine. The interviewee must ask for more data and answer this part mostly qualitatively.

The third part is optional. It is an extension of the case based on a possible recommendation from the second part. The interviewee must calculate the amount of profit that the new product must generate in order to justify investing in a new machine. The interviewee should also sketch and interpret the elasticity curve.

The questions in the big boxes should be read aloud to the interviewee.

Short Solution

  • The client can best utilize their current capacity by producing 4” and 8” bags on the roller. This product mix has the highest yearly profit ($270K)
  • The client should not invest in a new bag machine because even if they sell 12” bags in 5 years, their profits cannot cover $150K in fixed costs.
  • However, investment in a new machine may make sense if our client can meet the annual demand of 12” bags and utilize the surplus capacity to grow revenue.

Detailed Solution

Paragraphs highlighted in green indicate diagrams or tables that can be shared in the “Case exhibits” section.

Paragraphs highlighted in blue can be verbally communicated to the interviewee.

Paragraphs highlighted in orange indicate hints for you how to guide the interviewee through the case.

The following structure provides an overview of the case:

I. Product/Capacity

The interviewee should ask about the following issues:

  • Capacity of the machine
  • Demand for each kind of product
  • Revenue / costs for each product
  • Production time for each product

Share Diagram 1 with an overview of the capacity and Table 1 with an overview of the product mix’s demand/profitability if asked.

1. What mix of products should our client produce?

Information to be shared if the interviewee specifically asks for it

  • 500 “bag-widths“ produced per hour per product type
  • Machine run time:
    • 20 hours per day
    • 5 days a week
    • 50 weeks per year

The interviewee should calculate the total annual profit and production time per product line.

Bags produced per hr

Total annual profit

Production Time

4” bags

# bags produced /hour = 500 x 6 = 3,000

Total annual profit = $0.02 x 9M = $180,000

8” bags

# bags produced /hour = 500 x 3 = 1,500

Total annual profit = $0.03 x 3M = $90,000

12” bags

# bags made /hour = 500 x 2 = 1,000

Total annual profit = $0.04 x 3M = $120,000

Machine run time = 20 hrs/day x 5 days/week x 50 weeks per yr
= 5000 hrs per yr

Share Table 2 with an overview of the solution when the interviewee is finished with the calculation or gets stuck.

Main Conclusion

Under current capacity constraints (5000 hours/year), our client should produce 4” and 8” bags. This product mix generates the highest profit ($270k/year)

II. New Machine

2. Should the client invest in another roller? ‚Äč

Information that can be shared if inquired by the interviewee:

  • Cost of new roller = $750,000
  • Payback needed = 5 yrs
  • The roller will add an additional 5,000 hrs of machine run time
  • Mature market, no dramatic changes
  • Throughput growing at 2% due to efficiency of new roller

The interviewee should realize that if the new roller is able to meet the currently-unmet demand for 12 bags, our client’s profit would be $600K in 5 years.

Profit over 5 years

= Annual profit from 12" bags * 5 yrs = $120,000 * 5 = $600,000

However, the client must pay for the roller within 5 years. There is a profit shortfall of $150K.

Unrecovered investment

= Profit over 5 yrs - Cost of new roller = $600,000 - $750,000

= $150,000

At the current demand level, 2,000 machine production hours will NOT be used.

Annual unused capacity of new roller

= Machine run time - Capacity needed to meet 12" bags demand

= 5,000 - 3,000 hrs = 2,000 hrs

3. Why might it be a good idea to invest in a new machine?

Possible answers:

  • The demand growth rate could exceed 2%
  • Since the current market is mature, we could introduce a new product
  • We can rent out surplus machine production hours to increase revenue
  • Prices must increase to increase revenue

III. New Product

4. If we were to produce a new bag, what annual profit is required in order to justify investing in a new roller?


The client’s R&D team has just come out with a new bag. It’s a 2-in-1 bag, one side holds your sandwich and the other side holds your chips or lettuce to keep things from getting soggy. This bag is 6”.

Information to be shared if inquired by the interviewee:

  • There is no lag time between production and market acceptance.
  • Unrecovered investment from new roller = $150K
  • Payback period = 5 years

Additional profit needed

Possible ways to gain $30,000 per year in profit from a new product:

  • $0.03 profit per bag at 1M bags
  • $0.015 profit per bag at 2M bags
  • $0.01 profit per bag at 3M bags

If the interviewee does NOT suggest combinations, ask them to suggest a profit per bag and the corresponding sales volume required.

5. Draw the graph that represents the different profit/quantity combinations that would justify an investment in a new roller. Does this curve have any end points for our client given that the new machine will produce 6” bags @ 4 bags per bag-width for 2000 hours per year?

Share Diagram 3 with the interviewee.

Key Insights

Yes, there are two end points:

  • The lower limit of demand depends on price sensitivity. A higher profit margin such as $1 per bag is not feasible as production quantities wouldn’t be worth it.
  • The maximum demand we can serve depends on our production capacity. With the new roller, we can produce up to 4M of the new type of bag every year.

Bags made per hr

Unused capacity = 2,000 hrs per year

Maximum production level

IV. Conclusion

At the end of the case, the interviewee should come to the following conclusions:

  • The client can best utilize their current capacity by producing 4” and 8” bags on the roller because the combined profitability from this product mix is highest at $270K per year.
  • The client should NOT invest in a new bag machine because they cannot pay for the machine within 5 years. (They will still owe $150K.)
  • However, investment in a new machine may make sense if we are able to meet the annual demand of 12” bags and find a way to monetize the machine’s surplus capacity.

Difficult Questions

If we introduce a new product, what risks should we take into account?

Possible answer:

  • The new product may cannibalize the sales of our existing products. Thus, it may be harder to achieve the profit required to pay for the new machine within 5 years.
  • Since the machine produces two different kinds of products, there may be higher operations and maintenance costs.

More questions to be added by you, interviewer!

At the end of the case, you will have the opportunity to suggest challenging questions about this case (to be asked for instance if the next interviewees solve the case very fast).

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Case exhibits

Case Structure

Production Capacity

Profitability and Demand by Product Type

Total annual profit per product line

Possible profit/quantitiy combinations

Possible profit/quantity combinations