MA 132

Declining Prices, Profits, and Graphing

Introduction to Maple

Maple is a symbolic language, which means that it thinks differently from a spreadsheet. A spreadsheet thinks in data, and a symbolic program thinks in symbols.

Open a Maple window.
Try a few commands:

sin(0);

The ; has to appear at the end of your line. Notice it only gives you a zero if you typed a zero. What happens if you type an "oh" instead of a zero? (Try it!)

sin(Pi);

Maple is clever about some things. For example, it thinks of Pi as the ratio of the circumference of a circle to its diameter. But it is particular. If you type in

sin(pi);

then Maple doesn't think that pi is anything other than a Greek letter. This is because

Maple is case-sensitive
Maple has certain "reserved words" which have special meanings, and Pi is one of them.

Try typing

sin(Pi/4);

Notice that your answer is not given as a floating-point (decimal) number, but symbolically. If you want a floating-point number, try

sin(3.14159/4);

Maple can do a lot of the symbol manipulation that you had to do in your Calculus class. For instance, find the derivative of sin(x) and make a plot of sin(x):

sin(x);
diff(sin(x),x);
plot(sin(x),x=0..2*Pi);

So in our suits problem, if we have a profit function of -0.05x²+111x-10,000, we can plot it with

plot(-.05*x^2+111*x-10000,x=0..2500);

and we can find the derivative P'(x) by typing

diff(-.05*x^2+111*x-10000,x);

Once we see what the answer is, we can copy and paste to figure out when the derivative would be zero:

solve(-0.10*x+111=0,x);

and the answer should be 1110. Reality check: does that look like the maximum on your graph?

There is a nice way to plug in numbers in Maple. To find out what the profit would be at the x which gives the maximum profit, substitute x=1110 into P(x):

subs(x=1110,-.05*x^2+111*x-10000);

which should give $51,605.

Commands/features you have learned in Maple:

;
Pi
case sensitivity
symbolic versus floating-point
plot
diff
solve
subs