Natalia, a new MBA graduate, recently took a position with OU 3D Prosthetics, a small healthcare manufacturer which specializes in making prosthetic hands. Their produets provide individuals who have lost a hand due to injury, development issues, or other diseases, the ability to pick-up objects and function in everyday activities. Given the current scale of their operations, OU 3D Prosthetics uses 3D printing to produce prototypes, which they then sell to hospitals and healthcare providers around the country. These prototypes are fully functioning models that demonstrate the abilities of the final product, which allow patients, along with their doctors, to determine whether they want to pursue a prosthetic hand from OU 3D Prosthetics. OU 3D Prosthetics provides two different versions of prototypes, which differ in their level of detail: Model B is a basic model, and Model X is a higher-end version with greater durability and a more accurate representation of the final product. The basic process for producing the two prototypes consists of the same three steps: setup, printing, and assembly. During setup, an operator prepares the thermoplastic material polylactide material for a single unit. In the printing step, the machines conduct the 3D printing of the prototypes, which includes the main hand, along with components for fingers, joints, and other details (this printing step can be done in parallel with the setup step). Lastly, two separate assembly departments handle the process of assembling the components of the two prototypes. The basic process for producing the two prototypes consists of the same three steps: setup, printing, and assembly. During setup, an operator prepares the thermoplastic material polylactide material for a single unit. In the printing step, the machines conduct the 3D printing of the prototypes, which includes the main hand, along with components for fingers, joints, and other details (this printing step can be done in parallel with the setup step). Lastly, two separate assembly departments handle the process of assembling the components of the two prototypes. Table 1 shows the amount of time needed for each prototype. For example, one model B requires 0.25 hours for printing (which accounts for the number of printers and operators, etc). The operators can work for 800 hours each month for setups. Similarly, the 3D printers can print for 800 hours each month. The model B assembly department has a monthly capacity of 1900 units. The model X assembly department has a monthly capacity of 1400 units. Currently, OU 3D Prosthetics is producing and selling 400 units of model B and 1400 units of model X per month. Table 1: Time Requirements (hours per unit) Table 1: Time Requirements (hours per unit) Natalia, in her new role, was given the task of determining how many units of each prosthetic prototype to produce to maximize profits. Model B prototypes are sold for $1800, and Model X prototypes are sold for \$2100. OU 3D Prosthetics' operation is fairly small, but management believes that its prices must be fixed at these levels due to industry rules and standards. However, they forecast that they can sell as many of the prototypes as they can produce at these prices. You should answer the following Q1-Q4 questions based on the case above. You do not need to worry about Tables 2 and 3 for these questions. You should use the Excel template I posted and submit it with this document. 1. [2 pts] Given the current production levels, what is the current revenue/month? 2. [2 pts] Provide your LP algebraic formulation setup, including a) an objective function, b) decision variable(s), and c) constraints. Assume that the objective is to maximize the revenue. Be concise. 3. [2 pts] Provide the optimal production quantity for Model B and X and the total revenue. You must write your final answers here and provide your Excel file. 4. [2 pts] Now, they have an option to increase the maximum available setup time and/or the maximum available printing time by one unit hour each (e.g, hiring more employees). Which one(s) should they increase? Why? Management met with Natalia to discuss next month's operating plan. Although the prototypes are selling well, the overall profitability of the company was a concern. The company's engineer, Bob, suggested that the current printing of model B's should be cut back. "Model B's are sold for $1800 per unit, but our costs are $1839. Even though we're only selling 400 units a month, we're losing money on them." The financial controller disagreed, stating that the main problem was the Model B assembly department trying to absorb a large overhead with a small volume. "The model B units are making a positive contribution to overhead. Even though it doesn't cover all the fixed costs, we would be worse off with fewer units." The costs of the two prototypes are given in Tables 2 and 3 . What should Natalia recommend to management? Table 2: Standard Costs \begin{tabular}{|c|c|c|c|c|} \hline & \multicolumn{2}{|c|}{ Model B } & \multicolumn{2}{|c|}{ Model X } \\ \hline Variable Costs & & & & \\ \hline Materials & 1000 & & 1200 & \\ \hline Setup & 115 & & 125 & \\ \hline Printing & 180 & & 260 & \\ \hline Assembly & 245 & & 270 & \\ \hline Subtotal Variable costs & & 1540 & & 1855 \\ \hline Overhead (see Table 3) & & & & \\ \hline Setup & 69 & & 68 & \\ \hline Printing & 30 & & 59 & \\ \hline Assembly & 200 & & 61 & \\ \hline Subtotal Overhead & & 299 & & 188 \\ \hline Total & & 1839 & R & 2043 \\ \hline \end{tabular} Table 3: Overhead Budget Fixed Overhead per Month ('000s) Note on Tables 2 and 3: The overhead cost in table 2 is distributed using activity-based cost principles. For example, at current production levels, printing requires 100 hours for model B(0.25400) and 700 hours for model X(0.501400 ). Therefore, since printing nuns 800 hours a month, 12.5% of the time is spent on model B and 87.5% spent on model X, and the $95,000 fixed overhead for printing is thus distributed as $11,875($95,00012.5%) to model B and $83,125($95,00087.5%) to model X. The fixed overhead per unit of output for printing is finally allocated as $29.60($11,875/400) for model B and $59.38($83,125/1400) for model X). Now, you should answer the following Q5 question. Once again, you should use the Excel template I posted and submit it with this document. 5. [2 pts] The objective is to maximize the profit, not the revenue this time. What should Natalia recommend to management? Be specific. Natalia, a new MBA graduate, recently took a position with OU 3D Prosthetics, a small healthcare manufacturer which specializes in making prosthetic hands. Their produets provide individuals who have lost a hand due to injury, development issues, or other diseases, the ability to pick-up objects and function in everyday activities. Given the current scale of their operations, OU 3D Prosthetics uses 3D printing to produce prototypes, which they then sell to hospitals and healthcare providers around the country. These prototypes are fully functioning models that demonstrate the abilities of the final product, which allow patients, along with their doctors, to determine whether they want to pursue a prosthetic hand from OU 3D Prosthetics. OU 3D Prosthetics provides two different versions of prototypes, which differ in their level of detail: Model B is a basic model, and Model X is a higher-end version with greater durability and a more accurate representation of the final product. The basic process for producing the two prototypes consists of the same three steps: setup, printing, and assembly. During setup, an operator prepares the thermoplastic material polylactide material for a single unit. In the printing step, the machines conduct the 3D printing of the prototypes, which includes the main hand, along with components for fingers, joints, and other details (this printing step can be done in parallel with the setup step). Lastly, two separate assembly departments handle the process of assembling the components of the two prototypes. The basic process for producing the two prototypes consists of the same three steps: setup, printing, and assembly. During setup, an operator prepares the thermoplastic material polylactide material for a single unit. In the printing step, the machines conduct the 3D printing of the prototypes, which includes the main hand, along with components for fingers, joints, and other details (this printing step can be done in parallel with the setup step). Lastly, two separate assembly departments handle the process of assembling the components of the two prototypes. Table 1 shows the amount of time needed for each prototype. For example, one model B requires 0.25 hours for printing (which accounts for the number of printers and operators, etc). The operators can work for 800 hours each month for setups. Similarly, the 3D printers can print for 800 hours each month. The model B assembly department has a monthly capacity of 1900 units. The model X assembly department has a monthly capacity of 1400 units. Currently, OU 3D Prosthetics is producing and selling 400 units of model B and 1400 units of model X per month. Table 1: Time Requirements (hours per unit) Table 1: Time Requirements (hours per unit) Natalia, in her new role, was given the task of determining how many units of each prosthetic prototype to produce to maximize profits. Model B prototypes are sold for $1800, and Model X prototypes are sold for \$2100. OU 3D Prosthetics' operation is fairly small, but management believes that its prices must be fixed at these levels due to industry rules and standards. However, they forecast that they can sell as many of the prototypes as they can produce at these prices. You should answer the following Q1-Q4 questions based on the case above. You do not need to worry about Tables 2 and 3 for these questions. You should use the Excel template I posted and submit it with this document. 1. [2 pts] Given the current production levels, what is the current revenue/month? 2. [2 pts] Provide your LP algebraic formulation setup, including a) an objective function, b) decision variable(s), and c) constraints. Assume that the objective is to maximize the revenue. Be concise. 3. [2 pts] Provide the optimal production quantity for Model B and X and the total revenue. You must write your final answers here and provide your Excel file. 4. [2 pts] Now, they have an option to increase the maximum available setup time and/or the maximum available printing time by one unit hour each (e.g, hiring more employees). Which one(s) should they increase? Why? Management met with Natalia to discuss next month's operating plan. Although the prototypes are selling well, the overall profitability of the company was a concern. The company's engineer, Bob, suggested that the current printing of model B's should be cut back. "Model B's are sold for $1800 per unit, but our costs are $1839. Even though we're only selling 400 units a month, we're losing money on them." The financial controller disagreed, stating that the main problem was the Model B assembly department trying to absorb a large overhead with a small volume. "The model B units are making a positive contribution to overhead. Even though it doesn't cover all the fixed costs, we would be worse off with fewer units." The costs of the two prototypes are given in Tables 2 and 3 . What should Natalia recommend to management? Table 2: Standard Costs \begin{tabular}{|c|c|c|c|c|} \hline & \multicolumn{2}{|c|}{ Model B } & \multicolumn{2}{|c|}{ Model X } \\ \hline Variable Costs & & & & \\ \hline Materials & 1000 & & 1200 & \\ \hline Setup & 115 & & 125 & \\ \hline Printing & 180 & & 260 & \\ \hline Assembly & 245 & & 270 & \\ \hline Subtotal Variable costs & & 1540 & & 1855 \\ \hline Overhead (see Table 3) & & & & \\ \hline Setup & 69 & & 68 & \\ \hline Printing & 30 & & 59 & \\ \hline Assembly & 200 & & 61 & \\ \hline Subtotal Overhead & & 299 & & 188 \\ \hline Total & & 1839 & R & 2043 \\ \hline \end{tabular} Table 3: Overhead Budget Fixed Overhead per Month ('000s) Note on Tables 2 and 3: The overhead cost in table 2 is distributed using activity-based cost principles. For example, at current production levels, printing requires 100 hours for model B(0.25400) and 700 hours for model X(0.501400 ). Therefore, since printing nuns 800 hours a month, 12.5% of the time is spent on model B and 87.5% spent on model X, and the $95,000 fixed overhead for printing is thus distributed as $11,875($95,00012.5%) to model B and $83,125($95,00087.5%) to model X. The fixed overhead per unit of output for printing is finally allocated as $29.60($11,875/400) for model B and $59.38($83,125/1400) for model X). Now, you should answer the following Q5 question. Once again, you should use the Excel template I posted and submit it with this document. 5. [2 pts] The objective is to maximize the profit, not the revenue this time. What should Natalia recommend to management? Be specific