you need to answer question 3 only
Problem Set 3 [Updated] Update: Two notes (Note 1 and Note 2) added on 11/2 just to clarify the questions. Question 1: Consider a plant that manufacturer widgets – call it the Boiler Widget Factory. The manufacturing set-up involves an assembly line with three stations, each staffed with one worker. The worker at Station 1 starts the manufacturing process for each widget and takes 20 minutes to carry out the tasks assigned. Upon completion of the tasks at Station 1, the semi-finished widget is passed on to the worker at Station 2, who requires 30 minutes to complete the tasks assigned. The widget is finished at Station 3, where the worker takes 10 minutes. Now consider all the material costs during the manufacturing process. It is estimated that the cost of raw material is $10/widget. The labor costs are $12/hour. All other costs for the factory are fixed and amount to $5,000/month. The factory operates 8 hours a day and on average 20 days a month. It has a long-term contract with an exclusive buyer who pays $60/widget. The management is considering replacing the manual assembly line by a newly developed robot in the market. The robot can do the tasks performed by all three workers sequentially and produce one widget in 40 minutes, whereas the manual processing time is 60 minutes per widget. The fixed costs of the factory will remain the same, but the labor costs will be eliminated. The cost of leasing the robot is $2000 per month. In addition, the robot needs to be serviced and maintenance will cost $2,500/month. Due to its proximity to residential areas, the factory can only operate for 8 hours a day, which the robot manufacturer suggests is ideal to ensure optimal performance in terms of wear and tear. It turns out that the factory would still operate 20 days a month to allow for preventative maintenance and because the owner does not want to spend his weekends operating robots to churn out more widgets. What would you recommend? Is it profitable to replace the current manual line by this robot? Show your calculations. Note 1: The cost rate $12/hour is for one worker. Each worker is paid at the rate of $12/hour. Question 2: Company THEGOAL has just received an order for making three different products, A, B and C. Each product is required to be processed on two machines: X and Y. The following table summarizes the requirements for the three products: Product A Product B Product C Demand 2,000 1,000 500 Hours required on X per unit 2 3 1 Hours required on Y per unit 1 1 1 The revenue and the material costs for the products are as follows: Product A Product B Product C Revenue per unit $2,000 $2,500 $,1000 Material cost per unit $1,200 $1,600 $500 Q1: What is the total profit (Revenue – Material Cost) if the company could produce and meet the entire demand for all 3 products? Q2: To answer this question, assume that the capacity of machine X is 6,000 hours and the capacity of Y is 4,000 hours. Which machine is the bottleneck? Q3: Clearly, there is not enough capacity to meet the entire demand for all 3 products. So, there will be at least one product whose demand will not be met. The company selects production quantities to maximize the total profit. 1. Identify one product whose demand will not be met. 1. What are the optimal production quantities? 1. By how much will the profit go up if the company had one extra hour of X? 1. By how much will the profit go up if the company could sell one more unit of Product C? Note 2: In answering parts c and d, assume that a fraction of a unit can be produced and sold. You don’t need to round up (or round down) any production quantity.