Cases Case 16 Hospital Supply Inc Produce

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Cases Case 16-1 Hospital Supply, Inc. Hospital Supply, Inc., produced hydraulic hoists that were used by hospitals to move bedridden patients. The costs of manufacturing and marketing hydraulic hoists at the company's normal volume of 3,000 units per month are shown in Exhibit 1. EXHIBIT 1 Costs per Unit for Hydraulic Hoists Questions The following questions refer only to the data given in Exhibit 1. Unless otherwise stated, assume there is no connection between the situations described in the questions; treat each independently. Unless otherwise stated, assume a regular selling price of $4,350 per unit. Ignore income taxes and other costs not mentioned in Exhibit 1 or in a question itself. 1. What is the break-even volume in units? In sales dollars? 2. Market research estimates that monthly volume could increase to 3,500 units, which is well within hoist production capacity limitations, if the price were cut from $4,350 to $3,850 per unit. Assuming the cost behavior patterns implied by the data in Exhibit 1 are correct, would you recommend that this action be taken? What would be the impact on monthly sales, costs, and income? 3. On March 1, a contract offer is made to Hospital Supply by the federal government to supply 500 units to Veterans Administration hospitals for delivery by March 31. Because of an unusually large number of rush orders from its regular customers, Hospital Supply plans to produce 4,000 units during March, which will use all available capacity. If the government order is accepted, 500 units normally sold to regular customers would be lost to a competitor. The contract given by the government would reimburse the government's share of March production costs, plus pay a fixed fee (profit) of $275,000. (There would be no variable marketing costs incurred on the government's units.) What impact would accepting the government contract have on March income? 4. Hospital Supply has an opportunity to enter a foreign market in which price competition is keen. An attraction of the foreign market is that demand there is greatest when demand in the domestic market is quite low; thus, idle production facilities could be used without affecting domestic business. An order for 1,000 units is being sought at a below-normal price in order to enter this market. Shipping costs for this order will amount to $410 per unit, while total costs of obtaining the contract (marketing costs) will be $22,000. Domestic business would be unaffected by this order. What is the minimum unit price Hospital Supply should consider for this order of 1,000 units? 5. An inventory of 200 units of an obsolete model of the hoist remains in the stockroom. These must be sold through regular channels at reduced prices or the inventory will soon be valueless. What is the minimum price that would be acceptable in selling these units? 6. A proposal is received from an outside contractor who will make 1,000 hydraulic hoist units per month and ship them directly to Hospital Supply's customers as orders are received from Hospital Supply's sales force. Hospital Supply's fixed marketing costs would be unaffected, but its variable marketing costs would be cut by 20 percent (to $220 per unit) for these 1,000 units produced by the contractor. Page 483Hospital Supply's plant would operate at two-thirds of its normal level, and total fixed manufacturing costs would be cut by 30 percent (to $1,386,000). What in-house unit cost should be used to compare with the quotation received from the supplier? Should the proposal be accepted for a price (i.e., payment to the contractor) of $2,475 per unit? 7. Assume the same facts as above in Question 6 except that the idle facilities would be used to produce 800 modified hydraulic hoists per month for use in hospital operating rooms. These modified hoists could be sold for $4,950 each, while the variable manufacturing costs would be $3,025 per unit. Variable marketing costs would be $550 per unit. Fixed marketing and manufacturing costs would be unchanged whether the original 3,000 regular hoists were manufactured or the mix of 2,000 regular hoists plus 800 modified hoists was produced. What is the maximum purchase price per unit that Hospital Supply should be willing to pay the outside contractor? Should the proposal be accepted for a price of $2,475 per unit to the contractor? Introduction In the lab our objective was to experimentally measure strains in order to calculate the stresses at a particular point. The sensor used was a 45-degree strain gage rosette that was mounted to our cantilever beam specimen. The sensor ‘stretches’ as the part is loaded due to the strains developed. Due to this stretch, the sensor’s electrical resistance is altered. Using a computer machine from Vishay the strains can be recorded. The machine was tared to zero strain just before the weight was applied. It is necessary to measure the strain value between the longitudinal and transverse strain in order to calculate shear strain, since it is impossible to be measured directly. Experimental strains will then be converted into stresses and compared to hand calculations and finite element analysis results. A percent error analysis will be completed to compare results. Methods A 45-degree strain gage rosette was mounted on the cylindrical cantilever beam (See Figure A). Dimensions of the beam were recorded as well as the distance from the applied load to the strain gages. The beam was loaded with 4.5 pounds at the unfixed end of the pipe. A low weight was chosen due to the size of the structure and to avoid yielding of it. The Vishay machine was wired to the schematic and the three wires leading to the strain gages. The strain gage rosette measures longitudinal strain, transverse strain, and strain at a 45-degree angle. Using the strains measured through experimentation (ϵx , ϵy , and ϵ45) and by applying transformation equations the stresses can be calculated (σx , σy , and Ï„xy). The second method involved hand calculations by taking a cut at the element of interest (where the strain gage was applied). A moment and torque resulted due to the loading and were used to calculate the stresses. The calculated stresses were then converted into strains for comparison. The third method involved computer simulation. By creating the part in Solidworks and transferring it to Mechanical Simulation the stresses could be analyzed as well as the strains in the longitudinal and transverse directions. The node was carefully selected and results were pulled from the FEA analysis. Results Data Comparison (Stress in units of PSI) Experimental Hand Calculations FEA σ x σ y Ï„ xy Micro Strain-(Strain in units of in/in)(10-6) Experimental Hand Calculations FEA ϵ x ϵ y - γ xy Percent Error to Actual Results (FEA) Experimental Method Calculation Method σ x 11.10% 4.50% σ y 187% 100% Ï„ xy 4.10% 4.08% ϵ x 8.70% 0% ϵ y 28.57% 100% γ xy 43.24% 22.97% Reference the appendix for the hand calculations Discussion Finite element analysis provides the most accurate solution, so calculation and experimental methods were compared to those values for the percent error. For σx, the percent error was low for calculations but more error was in the experimental method. Hand Calculations give no stress or strain in the y-direction but FEA and experimental methods prove to show low strains, so the percent error for the stress and strains in the y-direction were 100%. Both the experimental and calculations had very low percent of error for the shear stress at the element. High percent error was found in the experimental and calculation methods for the shear strain. Causes for high percentages in error: Hand calculations disregard the weight of the actual specimen during static loading. Experimental specimen has pipe fittings around the bends whereas the model created in FEA consists of a smooth bent pipe. Imperfections in the test specimen and human error (such as measurements and placement of strain gage rosette) affect the experimental method. The hand calculations are more closely related to the FEA results compared to the experimental method. Appendix Figure (A) – Strain Gage Rosette on Specimen Figure (B) – Stress tensor at element Strain Gage Location of Element Force = 4.5 lb Figure (C) – Stress tensor at element Node of Interest 6 Multi- Cantilever Lab Abstract: The goal of this experiment was to was to understand strain measurement mechanism using electrical resistance strain sensor. From the measured strain values by using generalized Hooke’s Law (stress-strain relationship), applied stress in the structure will be evaluated. The second technique was the Finite Element Analysis (FEA) software. This technique required the use of the programs, AutoCAD and Mechanical Stimulation, in order to analyze the material of this experiment. The material can then be determined to see if it has the ability to resist or not as well as if the material is good enough to have this kind of load. The material can then be determined to see if it has the ability to resist or not as well as if the material is good enough to have this kind of load. Figure1: Solid work Drawing Introduction: A strain gage is a sensor whose resistance varies with applied force; It converts force, pressure, tension, weight, etc., into a change in electrical resistance which can then be measured. When external forces are applied to a stationary object, stress and strain are the result. Stress is defined as the object's internal resisting forces, and strain is defined as the displacement and deformation that occur. Figure2: Strain Gage Indicator Method: Our goal was to collect the data by using the the electrical resistance strain gage. First we have connected the red gage lead to the red terminal, second we connected white gage to the white terminal and finally the black gage to the yellow terminal. After that we had to verify it is quarter bridge wiring and make the calibrate amp equal to zero, record our gage factor, select run to calibrate and then we placed the weight. Finally, we are ready to track the data and collect them. Last step was to draw the specimen on solidwork and then do simulation to get an accurate reading. Strain Gauge Reading Gauge Gauge Gauge Figure3: Table for Data Collection Finite Element Analysis (FEA): Finite Element Analysis was found to be the most accurate technique. SolidWork and Mechanical Stimulation were used in this method. The drawing of the specimen was inserted into Mechanical Stimulation after being drawn in SolidWork. After, the mesh of the specimen was fixed before adding nodal loads directed to the XYZ-axise and some nodal general constraint. Finally the analysis stimulation is run to find sigma x,y. Additionally, maximum stress and minimum stress were found. Lastly, it can now be determined that the material is good enough to have this type of load according to the calculations below. The figures below are the results of using FEA: figure4: Sigma X Figure5: Sigma Y Figure6: Sigma XY Figure7: Fixed Forces Figure8: Applied forces Mathcad Calculations: Dicussion & Conclusion: In the laboratory we have learned how to use and understand strain measuring mechanism using electrical resistance strain sensor. Strain gauges are devices whose resistance changes under the application of force or strain. They can be used for measurement of force, strain, stress, pressure, displacement. After, doing comparing the calculations by hand and FEA we can see that there is no much different between them. For example, Sigma X was found to be 295.4 psi by hand calculation and by Sigma X was FEA was 324.7 psi in FEA. Finally, after finding sigma x,y and xy plus the maximum and Minimum point we can say that we have completed all the requirements for this laboratory. To better understand the stress and strain distribution in structural components, precise measurement using strain gauges combined with computational methods such as Finite Element Analysis (FEA) is essential. The experiment demonstrated the compatibility of experimental data, hand calculations, and FEA results, emphasizing the significance of integrating multiple methods for comprehensive stress analysis (Zhou et al., 2019). The errors observed in the experimental method highlight the importance of specimen preparation and measurement accuracy in experimental stress analysis (Saxena & Agarwal, 2020). In particular, discrepancies in strain measurements reinforce the need for meticulous calibration and installation of strain gauges to minimize human error (Liu & Zhang, 2021). The application of FEA provides a powerful tool for predicting stress and strain distributions, especially in complex geometries where analytical methods become insufficient (Zienkiewicz & Taylor, 2005). The combination of experimental and numerical approaches enhances the reliability of structural assessments, guiding safer and more economical design practices in engineering (Cook et al., 2009).In conclusion, understanding the behavior of materials under load via experimental strain measurements, hand calculations, and FEA is fundamental in mechanical and civil engineering, ensuring structures' safety, durability, and performance (Huebner et al., 2015). The integration of these methods exemplifies best practices in structural analysis, essential for advancing engineering design and research (Bathe, 2006).