Remote controlled miniature 3 frequencies generator

I am taking an electronics design class and we have a product-development project that is described below. I am trying to figure out how to go about it. The tricky part is the size of it. The frequency generation part has to be able to fit in about a matchbox and I have to spec out the parts required to built it.

Basically I need to be able to generate 3 different frequencies that are 5Vpp with 0.01-0.03mA. All 3 frequencies need to be independent of each other, meaning each one can be turned on/off irrelevant of the state of the others.

Example, all can run at the same time, or just 2 can run at the same time or any combination, etc. The circuit needs to be able to fit in a matchbox, be able to run for 60 mins and can be controlled in a very simple way from a remote control. I think the remote can be made to have simply 3 buttons , one for each frequency, where each button turns each frequency on or off.
Attached is also a small conceptual diagram that I came up with... Of course there might be other and more efficient or simple ways to do this ...Please advice! What is the simplest and smallest way built this? I will need to built a functional prototype of this by the end of the month.

Any input and help will be appreciated!
Thanks!

Since you sketched a sine-wave, did you study sine-wave oscillator circuits or look at the few different sine-wave oscillator circuits in Google?

Are you allowed to purchase a wireless remote control system?

Have you studied or looked in Google at battery types and have you selected one?

Doesn't your teacher offer any guidance?? Why not! Oh, you are in *****?

The remote control can be purchased separately or at least a configurable version of it, the integration of the receiver part to the circuit i need to figure out. I am thinking of using a 5Volt Lithium-Ion battery as a power supply. For the frequency generating part, from researching, I think 3 XR2206CP chips could do...

http://pdf1.alldatasheet.com/datasheet-pdf/view/80503/EXAR/XR2206CP.html

OR Option 2 which would be a lot hard for me would be programming a microcontroller.

You have some good ideas.
Look at Sparkfun for wireless remote control.