A company wants to schedule the transportation of four machines. The machines will must place them in a single container of a maximum weight of 4 tonnes. Because of this limitation, the company wants to place as many machines as possible in the container with profit maximization objective. The following table shows the weights of the machines in tons and their corresponding value in tens of thousands of euros.

machines	M1	M2	M3	M4
Weight	1	2	2	1
Value	3	2	4	2

A. Formulate the problem as an integer programming problem. B. Design a greedy algorithm for the problem that finds the optimal solution for this snapshot. C. Will the algorithm in question B always give the optimal solution? Explain why the this algorithm always finds the optimal solution or formulate a counterexample.