I've been stuck on this exercise for some time now.

A manufacturer produces sacks of chicken feed from two ingredients, A and B. Each sack is to contain atleast

10 ounces of nutrient N1, atleast 8 ounces of nutrient N2 and atleast 12 ounces of nutrient N3.

Ingredient A contains, per pound: 2 ounces of nutrient N1, 2 ounces of nutrient N2 and 6 ounces of nutrient N3

Ingredient B contains, per pound: 5 ounces of nutrient N1, 3 ounces of Nutrient N2 and 4 ounces of nutrient N3.

If ingredient A costs 8 cents per pound and Ingredient B costs 9 cents per pound, how much of ingredient should the manufacturer use in each sack of feed to minimize his cost.

I've called ingredient A for X1 and ingredient B for X2, thus the total cost Z will be:

Z = 8X1 + 9X1

Since it must contain atleast 10 ounce of N1:

2 X1 + 5X2 >= 10 (greater or equal to)

Since it must contain atleast 8 ounce of N2:

2X1 +3X2 >= 8

Since it must contain atleast 12 ounce of N3:

6X1 + 4X2 >= 12

Since each sack must totally contain 30 ounce all together (10+8+12)

X1+ X2 = 30

Have i set up the proper constraints?

If not, what have i done wrong.

If so, how do i solve this geometrically?