The company also has the option to obtain additional units from a subcontractor, who has offered to supply up to 20,000 units per month in any combination of electric and battery-operated models, at a charge of $21.50 per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme’s production process.
a. What are the maximum profit and the corresponding make/buy levels? (Fractional decisions are acceptable.)
b. Suppose that Acme requires that the solution provided by the model be implementable without any rounding off. That is, the solution must contain integer decisions. What are the optimal make/buy levels?
c. Is the solution in part (b) a rounded-off version of the fractional solution in part (a)?
Sample solution
Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.
In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.
God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.
Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.
To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.
References
Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.
Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.
Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.
Sample Answer
Sample Answer
To solve this problem, we need to analyze the make-or-buy decision made by Acme. This involves calculating the costs associated with manufacturing the units in-house versus purchasing them from a subcontractor.
Part (a): Maximum Profit and Corresponding Make/Buy Levels
Given Information:
– Cost of manufacturing in-house: Assume it is represented by ( C_m ) (the actual cost needs to be provided for precise calculations).
– Cost of purchasing from subcontractor: $21.50 per unit.
– Maximum units available from subcontractor: 20,000 units/month.
– Total demand: Assume it is represented by ( D ) (the demand must be provided for precise calculations).
Steps:
1. Define variables:
– Let ( x ) be the number of units produced in-house.
– Let ( y ) be the number of units purchased from the subcontractor.
2. Constraints:
– ( x + y = D )
– ( y \leq 20,000 )
3. Profit Function:
– Profit = Revenue – Costs
– Revenue = Selling price per unit (assume ( P )) * Total number of units sold.
– Costs = In-house production cost + Cost of buying units.
4. Optimal Levels:
Based on these equations, we can calculate the maximum profit by balancing the production and purchase levels while taking into account the total demand and constraints.
Part (b): Optimal Make/Buy Levels with Integer Decisions
When requiring integer solutions, we need to round off the fractional values obtained in part (a) to the nearest whole numbers. The process involves:
1. Re-evaluating the profit function, but with integer constraints.
2. Using integer programming techniques to solve the optimization problem.
3. Checking for feasibility, ensuring that ( x + y ) still meets total demand and that ( y ) does not exceed 20,000.
Steps:
1. Use a linear programming solver or integer programming method to determine values for ( x ) (in-house production) and ( y ) (subcontracted units).
2. Ensure that both ( x ) and ( y ) are integers and satisfy all constraints.
Part (c): Comparison of Solutions
To determine if the solution in part (b) is a rounded-off version of the fractional solution from part (a):
1. Analyze both solutions:
– Compare the integer solution with the fractional solution derived in part (a).
– Check if rounding off the fractional solution leads directly to the integer solution or if adjustments were needed.
2. Conclusion:
If the integer solution can be derived directly from rounding off without violating any constraints and maximizing profit, then it can be considered a rounded-off version. If adjustments were made, it is not merely a rounding but rather an altered solution based on integer constraints.
Conclusion
The analysis above provides a structured approach to solving Acme’s make-or-buy problem. By establishing profit functions, constraints, and utilizing optimization techniques, we can determine the best approach to maximize profits while adhering to production capabilities and demand requirements. Each part of this analysis builds upon the previous calculations, leading to informed decision-making for Acme.
To provide exact numeric answers, specific values for costs, selling price, and total demand need to be inputted into the equations.
