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?