Cost/Yield Math Task

[SWood]

I am confused about the next step of this math assignment. Here is what I have so far:

I have a part-time job delivering packages. My current employer pays me $300 per week to deliver packages. I work 20 hours a week and deliver an average of 8 packages per day. I discovered that my competitior pays its employees $10 an hour in addition to paying the $2 per package delivered.

I am trying to compare employers to find where I can make the most money and work the least amount.

The next sections asks me to discuss two cost/yield options that are being considered...

 

[mmm4444bot]

My current employer pays me $300 per week

I discovered that my competitior pays its employees $10 an hour [plus] $2 per package

My understanding of your scenario might not be correct. Why do you refer to a business for whom you do not work as your competitor?

You currently have a 20-hr work week, but how many days do you work per week? We need to know, in order to determine the total number of packages that you deliver each week. (You stated eight packages delivered per day.)

For the purposes of comparison, are we to assume that you would continue working 20 hours per week, if you were to switch employers? (I'm not sure why you're thinking that you might work less hours somewhere else.)

Did you provide all of the given information, in this exercise?

Please clarify.

 

[SWood]

4 days a week (5 hours per day) - 8 packages a day

And 'a' competitor, not 'my' competitor

This is only one section the assignment.
After stating 2 cost/yield options - I need to develop algebraic equations with clearly defined variables to represent the cost/yield of each option. I then have to explain my rasoning, solve the equations and depict the situation graphically.

Can you help?

 

[mmm4444bot]

?
It looks like weekly pay is a function of two variables: hours worked and packages delivered.

Here's a generic formula for weekly gross earnings, in this scenario.

w = A*h + B*p

The symbols w, h, and p are variables.

The symbols A and B are parameters (constants that change, from one employer to another).

w = weekly gross pay

h = number of hours worked in one week

p = number of packages delivered in one week

A = employee's hourly wage

B = employee's flat-rate pay per delivered-package

EG:

I work for a package-delivery joint that pays me $17.50 per hour plus an additional flat-rate of $4 per delivery.

In other words, for this employer:

A = 17.5

B = 4

Therefore, with this employer, a formula for my weekly gross earnings (w) in terms of the number of hours that I work during a week (h) and the number of packages that I deliver during the same week (p) is:

w = 17.5h + 4p

Let's say that I work 35 hours in one week, and I deliver 60 packages.

h = 35

p = 60

w = 17.5(35) + 4(60)

w = 612.5 + 240

w = 852.5

My gross weekly earnings from this particular employer is $852.50 .

Does this seem along the lines of what you've been asked to do?

A cost/yield analysis by a prospective employee (for selecting an employer) involves expenses to the employee (i.e., the cost), yes?

Are there differing costs to you, as an employee, working at one package-delivery joint versus another, in your scenario?

 

[SWood]

Yes, that helped very much. Thank you.

I have determined that Company A takes 20 hours and 32 packages to make $300 and Company B (the competitor) takes 23 hours and 35 packages to make $300.

Now I need to depict the situation graphically, including:
- a depiction of each option on the same graph
-Clear labels of the cost/yield for both options
and
- the intersection of the cost/yield options (if one exists)

 

[mmm4444bot]

My current employer pays me $300 per week to deliver packages

I have determined that Company A takes 20 hours and 32 packages to make $300

I do not understand you.

Are you an employee earning $300 per week, or are you an employer running a company that makes $300 per week?

Perhaps, you are self-employed?

Please clarify.

?

Now I need to depict the situation graphically

Uh oh.

If we need to graph lines, then there can be no more than two variables.

Now I'm thinking that the flat-rate pay is unique only to this one prospective employer. Therefore, we need to eliminate p as a variable, and treat any extra pay based on the number of packages that you might deliver, working anywhere, as an extra constant that may or may not be needed, in a formula.

In other words, we're going to treat weekly gross as a function only of hours worked. It's just that one joint gives you a bonus (based on delivery numbers) because they don't pay as much per hour.

Rather than just handing you the weekly bonus on a silver platter, this exercise is apparently set up to make you calculate it, before writing the formula for the prospective employer.

(Of course, these are all assumptions, on my part. I don't know what your assignment is. I'm making guesses, based on what you've written.)

Let w1 = current weekly pay at $A/hr

Let w2 = prospective weekly pay at $B/hr plus some constant

w1 = A*h

w2 = B*h + C

where C is a constant that I'll let you figure out.

Hint: C = the extra amount of money that you get over 4 days from that flat-rate bonus pay.

Do you know how to graph lines in the xy-plane ?

In other words, are you familiar with the following famous formula ?

y = m x + b

If so, do you "see" the similarities ?

w1 = A h + 0

w2 = B h + C

Think h-axis (horizontal) and w-axis (vertical).

MY EDITS: Fixed day-number error (5 days to 4); added color coding on slope and vertical intercept; tweaked some ambiguous phrases

 

[SWood]

Okay, so I've got
w1=Ah w1=15(20)=300

w2=Bh+C (C being packages delivered)
w2=10(23)+35=300

So with y=mx+b

Do I have 2 sets of points to graph? As in, (20, 300) and (23, 300)
Or am I completely lost?

 

[mmm4444bot]

?

Hint: C = the extra amount of money that you get over 4 days from that flat-rate bonus pay.

(emphasis mine, naturally)

?

(C being packages delivered) This is not correct. C represents money.

I'm thinking that you might benefit, if you read my last response again.

C is not 35. C is a fixed dollar-amount.

Also, when determining the value of C, don't use 35 as the number of packages delivered per week. That's not correct, if there are eight deliveries on each of the four days.

And look! You added: (money earned from hourly wages) + (number of deliveries)

Does it make sense to add: $200 + 35 packages? How many dollars is that?

In other words, where have you hidden the $2 flat-rate? I'm not seeing the calculation of the bonus.

Please show your work on that part.

Finally, from where did you get the 23-hour value for h ?

?

am I completely lost?

Not completely.

Yes, you can plot (h, w) points.

Once you've got correct formulas, you can pick any number of hours for h, followed by calculating the values of w.

 

[Denis]

I am confused about the next step of this math assignment. Here is what I have so far:

I have a part-time job delivering packages. My current employer pays me $300 per week to deliver packages. I work 20 hours a week and deliver an average of 8 packages per day. I discovered that my competitior pays its employees $10 an hour in addition to paying the $2 per package delivered.

NOW: you are paid $15 per hour (20 * 15 = 300), regardless of number of packages you deliver;
the average of 8 packages per day is just a statistics.

NEW: if you work same number of hours, you'll earn $200 (20 * 10);
to make up the $100, you need to deliver 50 packages (50 * 2 = 100);
over 4 days means 12.5 packages per day

Since you want to work LESS, STAY where you are!

 

[SWood]

Thank you so much! You helped a ton!

The only section I am not sure what to write is when they ask me to discuss two cost/yield options at the beginning of the assignment.

Is that just the two equations we used???