Buckeye Novelties is a toy company that brought in a Fisher team to re-organize the supply chain of a new division start-up for two primary products: bobble head dolls of local sports figures and figurehead pencils. By designing a lean operation and re-negotiating vendor contracts, the Fisher team improved profitability on these items to $ 5 per doll and $ 3 (per package of 20 pencils), respectively.

The key production costs are Raw Material and Assembly Labor. Because of the higher assembly time on the dolls and limited facility space, the company decides to limit production of dolls to 7 units per week in order to have sufficient capacity to produce the figurehead pencils. Finally, one of the key improvements that the Fisher team introduced is the use of recycled material as an input. One of the specialty inputs for the bobble head doll is springs; they come carefully packaged in metal containers. This metal can be recycled and used as material input for the pencil figureheads. Since this is a special item and an unusual situation for the production floor, Springs are broken out separate from the Raw Material category above.

The company does have some financial and physical limitations, so the project team focused on profit improvement efforts, not expansion. For this reason, no overtime will be paid and no hires will be added during this startup period beyond the one specialist assigned to assemble both products. Her standard workweek is 40 hours. In an attempt to limit weekly Raw Material purchases to the physical limits of the facility, total inputs (expressed as an index of various items in pounds) are limited to 48 pounds.

Product Assembly Parameters Raw Material Usage

(Pounds)

Dolls- 5 hours/unit 3

Pencils- 2 hours/ unit (20) 6

For each bobble head doll, 2 springs are used. Based on the conversion of packaging material described above, every two springs ADD BACK 1 equivalent unit (in springs) of recyclable material for pencils. (Hint: Treat this as a - for the Springs constraint for pencils since it is not consumed but rather added back as additional raw material. This does not change the RM index relationship above.) One important issue is to balance metal material flow between purchased inputs and recycled input from the springs. The Team did calculations separately to determine that the weekly production process flow requires a minimum of 3 springs. This ensures stable and predictable demand for raw material orders.

Let X = bobble head dolls and Y = figurehead pencils (package of 20). What is the proper product mix in order to maximize profit?

The Long Range Business Plan

The pandemic accelerated demand for at-home recreation. Low cost novelties were particularly popular.

With current demand just about absorbing the full capacity of the Ohio plant, Buckeye Novelties looked at different options to expand. The big question hanging over an expansion decision is how certain and how sustainable the demand spike would be. So, a range of options was under consideration:

1. Expand only the existing plant
2. Build a new plant with updated technology
3. Do both
4. Do neither

Three demand forecasts were estimated: Optimistic at 30% likelihood, Moderate at 50%, and Poor at 20%.

The payoff matrix for this decision was developed by marketing and accounting in collaboration ($ shown are NPV in millions):

Decision	Optimistic	Moderate	Poor
Expand existing plant	4	2	1
Build new plant	9	5	-3
Expand + Build	12	4	-6
Do Nothing	0	0	0

Question:

Part 1 -Formulate the product mix problem

Part 2-

Develop a graphical solution using X as the horizontal axis and Y as the vertical axis. Requirements include:

• Carefully label each constraint
• Identify each corner point
• Highlight or cross-hatch the feasible region
• Plot one Level Curve at a value of Profit = $ 30
• Include back-up calculation to show each constraint line
• Develop an algebraic solution by enumerating all the Corner points.