Finding an optimal number of different containers that can be made of the required amount

Question

For example, 35ml needed where only 16ml and 10ml available. 35ml can be made with (3pcs of 16ml) = 48, (4pcs x 10ml) = 40 or (1 x 16ml, 2 x 10ml) = 36 but the optimal one is (1 x 16ml, 2 x 10ml) because there is only 1 = 36-35 space unlike others.

Update:

I was trying to use linear programming which may help to find x and/or y (finding the quantity) based on constraints but it's like I find it difficult to implement.

Constraints are:

Let z be the number of space
X and/or Y to be the quantity
16x + 10y >= 35
x>=0
y>=0

outcome = 16(1) + 10(2) >= 35

Answer 1

Let z be the excess

and x and y be the number of 16ml and 10ml bottles. So they are defined as integers

Let A be the desired Amount. So the optimization problem is

$Min$ $ z= 16x + 10y - A$ such that $x,y,z \ge 0$

$x,y$ are integers