1. Linear programming:
Solve the following integer linear program:
max wrt x1,x2,x3 for Z= 9x1 + 3x2 + 5x3;
subject to 5x1 + 2x2 + 5x3 ≤ 10;
x1, x2, x3 ∈ {0, 1}.
2. Suppose that there are k gold mines available for sale. The cost of each mine i is ci , etc. The amount of gold deposit in each mine i is vi . You have an amount M of money, give a mathematical model the problem of finding the most profitable set of mines to buy when it is not allowed to buy a portion of a mine.