1. Explain why any combination of , and can also be achieved by a combination of just , and . For example, show how to make the custom mix using only , , and .

Your solution needs to show how you used Matlab to solve this problem. The final result needs to be clearly stated in a sentence.

2. Why will there still be mixes that cannot be physically produced from this set of five basic mixes? (Hint: Consider the signs of the scalar weights.) Give an example of such a mix.