RoxieApoxie
New member
- Joined
- Jun 24, 2011
- Messages
- 10
So, I'm basically seeing if what I am doing is correct, I think I have the right idea but I really have no idea.
The manager of a plant has been instructed to hire and train additional employees to manufacture a new product. She must hire a sufficient number of new employees so that within 30 days they will be producing 2500 units of product each day.
Because a new employee must learn an assigned task, production will increase with training. Suppose that research on similar projects indicates that production increases with training according to the learning curve, so that for the average employee, the rate of production per day is given by
DN/dt = be^-at
where N is the number units produced per day after t days of training. Because of experience with a very similar project, the manager expects the rate for this project to be
DN/dt =2.5e^-.05t
The manager tested her training program with 5 employees and learned that the average employee could produce 11 units per day after 5 days of training. On the basis of this information, she must decide how many employees to hire and begin to train so that a month from now they will be producing 2500 units of the product per day. She estimates that it will take her 10 days to hire employees. and thus she will have 15 days remaining to train them. She also expects a 10% attrition rate during this period
How many employees would you advise the plant manager to hire? check your advice by answering the following questions
1) Use the expected rate production and the results of the manager's test tp find the function relating N and t ---that is, N=N(t)
I'm assuming that this is the antiderivative, which would be N=-50e^-.05t+C, am I incorrect on this assumption?
2)Find the number of units the average employee can produce after 15 days of
training. How many such employees would be needed to maintain a production
rate of 2500 units per day?
Are we solving for C here? I guess I'm a little bit confused, I set up the equation so it would look like 2500 = -50e^-.05(15)+C and we go ahead and solve for C and that is 2500, so therefore their needs to be 2500 employees
3)Explain how you would revise this last result to account for the expected 10% attrition rate. How many new employees should the manager hire?
So ..Is that 2500 x .10 = 250 = 2500 -250 = 2250, therefore the manager should hire 2250 employees? Or.. no?
I appreciate the fact-checking!
The manager of a plant has been instructed to hire and train additional employees to manufacture a new product. She must hire a sufficient number of new employees so that within 30 days they will be producing 2500 units of product each day.
Because a new employee must learn an assigned task, production will increase with training. Suppose that research on similar projects indicates that production increases with training according to the learning curve, so that for the average employee, the rate of production per day is given by
DN/dt = be^-at
where N is the number units produced per day after t days of training. Because of experience with a very similar project, the manager expects the rate for this project to be
DN/dt =2.5e^-.05t
The manager tested her training program with 5 employees and learned that the average employee could produce 11 units per day after 5 days of training. On the basis of this information, she must decide how many employees to hire and begin to train so that a month from now they will be producing 2500 units of the product per day. She estimates that it will take her 10 days to hire employees. and thus she will have 15 days remaining to train them. She also expects a 10% attrition rate during this period
How many employees would you advise the plant manager to hire? check your advice by answering the following questions
1) Use the expected rate production and the results of the manager's test tp find the function relating N and t ---that is, N=N(t)
I'm assuming that this is the antiderivative, which would be N=-50e^-.05t+C, am I incorrect on this assumption?
2)Find the number of units the average employee can produce after 15 days of
training. How many such employees would be needed to maintain a production
rate of 2500 units per day?
Are we solving for C here? I guess I'm a little bit confused, I set up the equation so it would look like 2500 = -50e^-.05(15)+C and we go ahead and solve for C and that is 2500, so therefore their needs to be 2500 employees
3)Explain how you would revise this last result to account for the expected 10% attrition rate. How many new employees should the manager hire?
So ..Is that 2500 x .10 = 250 = 2500 -250 = 2250, therefore the manager should hire 2250 employees? Or.. no?
I appreciate the fact-checking!