1. PQ Problem: Notation note This example is based on an example case in the OM literature. Products are X, Y, and Z (not P, Q); resources are A, B, C, D, E; RM stands for raw material. A process flowchart (aka process flow diagram), graphing the path each product follows through the manufacturing process is shown below, where each products unit price, max weekly demand, and unit processing times data at process steps are indicated as well. Bearcat Enterprises can make and sell up to the limit of its weekly demand and there are no penalties for not being able to meet all the demand. Assume overhead costs do not need to be considered.

Consider the 3-product (X,Y,Z), 5-resource (A-E) example in the figure below:

Figure notes: Product X is sold at 90$/unit and its weekly demand is 50 units. Manufacturing of Product X starts by processing two separate RM2 units in resource A with ten minutes for each unit. One of these units goes to resource C and is processed for 15 minutes while the other one goes to resource D for 15 minutes processing. Then, those materials are joined to each other along with an RM1 unit and are processed in resource E for five minutes. Similar flows exist for Products Y and Z, which share some common components. For instance, a unit of the RM2 A D subassembly component of Product X can also be sent to resource E for 10 minutes to be combined with another subassembly component using RM3 to make Product Y

Suppose there are 40 hours = 2400 minutes per week available on each resource A thru E, with one worker per resource. Assume that all employees are salaried and weekly labor costs are charged at the rate of 10$/hour/resource, and do not depend on the production quantities or labor utilization.

Answer ANY THREE of parts a, b, c, d below:

1. Which workstation is the bottleneck? Explain that is, show relevant calculations / approach used to answer the question or explain the logic used to determine the bottleneck.

2. Calculate the bottleneck ratios and determine which product (X, Y, Z) is given higher (#1-highest, #2, #3-lowest) production priority by the bottleneck ratio method. Is this prioritization the same as that obtained using the unit profit method instead of bottleneck ratios?

3. Determine the production plan (number of units of X, Y, and Z produced weekly) using the bottleneck ratio method. Calculate the weekly net profit corresponding to your production plan including all specified costs.

4. Would you increase capacity on any resource using overtime paid at time-and-a-half (1.5 x 10 = 15$/hour)? If yes, on which resource(s) and for how long? If not, why not? Briefly explain your reasoning.