Production/Operations Management and Business Policy advice for Excelsior

[irnbru]

I've seen several people on here who have completed the CSU-Peublo 311 course. I was wondering if someone could assist with a problem. I am having a very hard time with these problems.
Here's the problem:

1. Sammy Sleaze has decided to illegally copy CD’s to sell in his CD store. There are several possible CD copiers that sales reps have shown him. Machine A has a fixed cost of $900 with a variable cost of $1 per unit. Machine B has a fixed cost of $3500 with a variable cost of $0.85 per unit. Machine C has a fixed cost of $10,000 with a variable cost of $0.40 per unit.

a. Mathematically calculate the point (in CD’s copied) at which the total costs are equal between machines A and B. You must show your work for full credit.

b. Mathematically calculate the point (in CD’s copied) at which the total costs are equal between machines A and C. You must show your work for full credit.

c. Mathematically calculate the point (in CD’s copied) at which the total costs are equal between machines B and C. You must show your work for full credit.

d. For each machine A, B and C, draw the total cost lines on the graph included. Label all important points. Please turn the page 90 degrees clockwise for best fit of the data on the graph. Neatness and proper scaling count.

e. Write a decision rule for selection of machines based on anticipated number of CD’s copied

I have all the excel OM software but there are so many files, I'm not sure which one to use, if any...Thank you so much for the assistance. Not really looking for the answers, I just can't figure this out.

Thanks again,

- Steve

Okie, the first question is asking how many cds will be produced when the amount of money thrown at both machines is the same. This means you are trying to find a single unknown, let's call it x.

The fixed costs are constant and will be treated as such. The variable costs depend on how many cds are produced.

For x number of cds, machine A will cost $900 plus however many cds are produced. So this becomes:

900 + 1*x

Machines B and C will cost respectively:

3500 + 0.85*x
10000 + 0.4*x

Since we want to find out how many cds will be produced when the cost is the same, for question a. we equate the costs of Machines A and B:

900 + x = 3500 +0.85x

An equation in one variable which we can solve for x:

0.15x = 2600
x=2600/0.15
x= -----.- repeating

So, when machines A and B produce -----.- cds, the cost is the same. Since we don't make a third of cds, round up to the nearest whole number, -----.

We can plug this value back into either cost equation to verify the cost is equivalent:

900 + (-----.-) = 3500 + 0.85(-----.-) = -----.- USD

The same process is used for questions b. and c.

Machine A and Machine C:

900 + x = 10000 + 0.4x

Solving for x leads us to x = -----.-

Machines B and C:

3500 + 0.85x = 10000 + 0.4x

Solving for x leads us to x = -----.-

Graphs

To draw the graph for each machine, just notice that Machine A's cost function (900 + 1*x) is a linear function. So, it will graph exactly like any function y = ax + b. In this case it has a gradient of 1 (45' angle) and will cut the y axis at b, which will be $900.

Can't remember how to do decision rules so hopefully someone else or google will do the work for you

Hope this helps.


edit: Just noticed you've been posting this question elsewhere, Stephen. Glad to have got in, first