linear programming

1a. What is the purpose for using linear programming?
1b. A nutritionist wishes her clients to have a daily minimum of 30 units of
vitamin A, 20 units of vitamin D, and 24 units of vitamin E. One dietary
supplement y1 costs $80 per kilogram ($80/kg) and provides 2 units of
vitamin A, 5 units of vitamin D, and 2 units of vitamin E. A second y2
costs $160/kg and provides 6 units of vitamin A, 1 unit of vitamin D, and
3 units of vitamin E.
i. Find an expression for the objective function.
ii. Write down all the constraints.