March 15, 2007
3:20 PM

Use Format → Style → to select the appropriate style for a cell.
        This cell is using text (Alt-7)
The next cell will use Input and will evaluate an expression.
    Click below this line to begin a new cell.

In[2]:=

Out[2]=

The above cell was evaluated when I pressed shift-enter.

Larson section p.2 no. 71 [p. 19]

Career Choice. An employee has two options for positions in a large corporation. One position pays $12.50 per hour plus an additional unit rate of $0.75 per unit produced. The other pays $9.20 per hour plus a unit rate of $1.30.
(a) Find linear equations for the hourly wages W in terms of x, the number of units produced per hour, for each of the options.
(b) Use a graphing utility to graph the linear equations and find the point of intersection.
(c) Interpret the meaning of the point of intersection of the graphs in part (b). How would you use this information to select the correct option if the goal were to obtain the highest hourly wage?

(a) Position One: W = 12.5 + .75x   where W is the hourly wage and x is the number of units produced per hour.

Position Two: W = 9.2 + 1.3x

Now to obtain graphs for these two formulae. I want the graphs to appear on the same axes.

Out[12]=

In[14]:=

Out[14]=

In[18]:=

Now to make these graphs more appealing. I only want the values of x to go from 0 to 10 and I want each graph to be a different color.

In[23]:=

In[24]:=

The two graphs appear to cross at the point x = 6.
The point of intersection can be determined as follows:

In[27]:=

Out[27]=

The two lines intersect at the point (6, 17)

When x is less than 6 the blue line (i.e. W1) is the larger, but when x is greater than 6 then W2 is larger. Thus, if one thinks that they can produce more than 6 units they should select option 2 as the best payment plan, otherwise they should select option 1. If they think they can produce exactly 6 units, then it makes no difference which plan they use.

There are some tricky formatting issues in the above having to do with the unique symbolism of Mathematica. I think it makes good sense at the beginning to simply copy the formulae and learn more about the underlying rationale as one becomes more familiar with the software.

Created by Mathematica  (March 15, 2007)