Task:

You manage the production process in the high$-$tech facility of Dale Computers Inc. The facility

consists of three different assembly lines $(1,2,3)$ making two different products, $x$ and $Y.$

Assembly Line $2$ is dedicated to the assembly of product $x,$ and assembly line $3$ is dedicated to

product Y$.$ Assembly Line $1$ can assemble both the products. The production process begins with

the procurement of raw materials from suppliers. Next, the raw materials are processed into six

independent subassemblies, A$-$F$,$ in separate work areas within the facility. Each product is then

assembled from these subassemblies in one of the assembly lines. Product $x$ involves the assembly

of subassemblies A$,$ B$,$ C$,$ and E$.$ Product Y requires that subassemblies B$,$ C$,$ D$,$ E$,$ and F be

assembled. Subsequent to assembly, each product is finished, customized $($painted and other options

added$),$ packaged and shipped. Current trends indicate that $20\%$ of product $x$ and $50\%$ of product $Y$

are customized.

Following are the capacities of the work areas producing the subassemblies:

The annual demands for the products are as shown below:

The capacities of the assembly lines and the finishing, packaging and customizing areas are as given

below:

Notes: $(1)$ Assume $52$ operating weeks$/$year$.$ Converting to weekly demand may be helpful.

$(2)$ Plan production to just meet the demand $($do not overproduce$).$

Question:With the current weekly demands of $1000$ for each product X and Y$,$ what is the current bottleneck resource? Show your calculations. $[$Note: Don$$t change demand yet$]$