Theory of Constraints
Playful Pens, Inc., makes a single model of a pen. The cartridge for the pen (which contains the ink) is manufactured on one machine. The cartridge holder (which you hold when you hold the pen) is manufactured on another machine. Monthly capacities and production levels are as follows:
$$
\begin{array}{lrr}
\hline & \text { Machine 1 (Cartridge) } & \text { Machine } 2 \text { (Holders) } \\
\text { Monthly capacity . . . . . } & 1,000,000 & 800,000 \\
\text { Monthly production ... } & 800,000 & 800,000
\end{array}
$$
The company could sell $1,000,000$ pens per month. The units (cartridge inside of holder) sell for $$\$ 10$$ each and have a variable cost of $$\$ 4$$ each. Fixed costs are $$\$ 4,000,000$$ per month.
Required
a. Is there a bottleneck at Playful Pens? If so, where is it?
b. Playful Pens's production supervisors state they could increase machine 2's capacity by 200,000 per month by producing holders on the weekend. Producing on the weekend would not affect the sales price. Variable cost per unit would increase by $$\$ 1$$ for those produced on the weekend because of the premium paid to labor. Fixed costs would also increase by $$\$ 800,000$$ per month. Should Playful Pens produce holders on the weekend?
c. Independent of the situation in requirement $(b)$, Playful Pens could expand the capability of machine 2 by adding additional workers to perform ongoing maintenance. This would increase its capacity by 100,000 holders per month. This would not affect sales price or fixed costs, but would increase variable cost to $$\$ 4.50$$ per unit for all units produced. Should Playful Pens expand machine 2's capability by adding these additional workers?