Linear Models for Financial Analysis

An employer pays $3,000 per month for renting office space, and pays a total of 12 employees (including yourself) $1,000 per month (each) plus a bonus of $10 for each unit of work completed by that employee that month.

Suppose also that your employer makes $18 (gross) per unit of work done by an employee. Use Profit = Revenue – Cost (P = R - C)[Total points: 16]

1. Suppose you complete 200 units this month. How much will you be paid? [1 pt]

2. Suppose all of your co-workers (on average) also complete 200 units this month. Find your boss’ profits. [1 pt]

3. Repeat 1 and 2 with an average of 300 units this month. [2 pt]

4. Find your monthly pay S in terms of x, the number of units of work you complete that month. [1 pt]

5. If all of your co-workers produce/sell (on average) x units per month, find the monthly profit P of your employer in terms of x. [1 pt]

Graph this equation [1 pt]* , and use the graph and the equation to determine how productive your employees have to be for your boss to:

(a) break even [1 pt]; 

(b) make $1,000 per month [1 pt]; 

(c) make $5,000 per month [1 pt];

In addition find the y-intercept and use that as one of your points.

What is the meaning of the x-intercept [1 pt] and the y-intercept [1 pt] (In this problem, the y-axis represents P (profit))? 

6. Due to the revenue from the units of work you completed, your employer is now able to rent a bigger office ($10,000 per month), and employ 50 employees (at the same wages). Find your boss’ profits P in terms of x [1 pt] (Do not graph) and answer parts a, b, and c from above [3 pt].

*Make x-axis x, # of units and make it into 25, 50, 75, 100, etc units.

Make y-axis P for profit and the divisions $1000, $2000, $3000, etc. Be sure to show negative values for profit but not for # of units