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Liverpool Sawmill, Inc. (LSI) purchases logs from independent timber contractors and processes the logs into three types of lumber products: Studs for residential buildings (walls, ceilings), Decorative pieces (fireplace mantels, beams for cathedral ceilings), Posts used as support braces (mine support braces, braces for exterior fences on ranch properties). The studs are sold as rough-cut lumber after emerging from the sawmill operating without further processing by LSI. Also, the posts require no further processing beyond the splitoff point. The decorative pieces must be planed and further sized after emerging from the sawmill. This additional processing costs $90,000 per month and normally results in a loss of 10% of the units entering the process. Without this planning and sizing process, there is still an active intermediate market for the unfinished decorative pieces in which the selling price averages$55 per unit. These products are the result of a joint sawmill process that involves removal of bark from the logs, cutting the logs into a workable size (ranging from 8 to 16 feet in length), and then cutting the individual products from the logs. The joint process results in the following costs of products for a typical month:

Direct materials (rough timber logs)$480,000Debarking (labor and overhead)50,000Sizing (labor and overhead)220,000Product cutting (labor and overhead)260,000Total joint costs$1,010,000\begin{matrix} \text{Direct materials (rough timber logs)} & \text{\$480,000}\\ \text{Debarking (labor and overhead)} & \text{50,000}\\ \text{Sizing (labor and overhead)} & \text{220,000}\\ \text{Product cutting (labor and overhead)} & \text{260,000}\\ \text{Total joint costs} & \text{\$1,010,000}\\ \end{matrix}

Product yields and average sales values on a per-unit basis from the joint process are as follows:

ProductMonthly Output of Materials at Splitoff PointFully Processed Selling PriceStuds78,000 units$5Decorative pieces4,000 units85Posts28,000 units26\begin{matrix} \text{Product} & \text{Monthly Output of Materials at Splitoff Point} & \text{Fully Processed Selling Price}\\ \text{Studs} & \text{78,000 units} & \text{\$5}\\ \text{Decorative pieces} & \text{4,000 units} & \text{85}\\ \text{Posts} & \text{28,000 units} & \text{26}\\ \end{matrix}

  1. Based on the information given for Liverpool Sawmill, allocate the joint processing cost of $1,010,000 to the three products using: a. Sales value at splitoff method, b. Physical-measure method (volume in units), c. NRV method. 2. Prepare an analysis for Liverpool Sawmill that compares processing the decorative pieces further, as it currently does, with selling them as a rough-cut product immediately at splitoff. 3. Assume Liverpool Sawmill announced that in six months it will sell the unfinished decorative pieces at splitoff due to increasing competitive pressure. Identify at least three types of likely behavior that will be demonstrated by the skilled labor in the planning-and-sizing process as a result of this announcement. Include in your discussion how this behavior could be influenced by management.

Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces with F1=32 N,θ1=30F_1=32 \mathrm{~N},\theta_1=30^{\circ} from the positive xx axis in the first quadrant, F2=55NF_2=55 \mathrm{N} along the positive xx axis and ,F3=41 N,θ3=60F_3=41 \mathrm{~N}, \theta_3=60^{\circ} from the positive xx axis in the fourth quadrant. What is the asteroid's acceleration direction relative to the positive direction of the xx axis?


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