Question 1165008: The Karo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen,
phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6
ounces of phosphate, whereas a pound of ingredient 2 contributes 2 ounces of nitrogen, 6
ounces of phosphate, and 1 ounce of potassium. Ingredient 1 costs PhP 3 per pound, and
ingredient 2 costs PhP 5 per pound. The company wants to know how many pounds of each
chemical ingredient to put into a bag of fertilizer to meet minimum requirements of 20 ounces
of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.
Answer by ikleyn(53339)   (Show Source):
You can put this solution on YOUR website! .
The Karo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium.
A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, whereas
a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium.
Ingredient 1 costs PhP 3 per pound, and ingredient 2 costs PhP 5 per pound.
The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer
to meet minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium
while minimizing cost.
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I will solve it mentally, on fingers.
First, obviously, we need to use two pounds of ingredient 2 to provide 2 ounces of potassium.
After that, we need to provide as minimum 20-2*2 = 16 ounces of nitrogen and 36-2*6 = 24 ounces of phosphate.
Next, it is also obvious, that for it, we should use as many pounds of ingredient 1 as possible, because
(a) ingredient 1 is cheaper, and
(b) each pound of ingredient 1 contains the same 6 ounces of phosphate as each pound of ingredient 2.
After these notices, it is clear that 24/6 = 4 pounds of the ingredient 1 should be used.
Thus we get this
ANSWER. 2 pounds of ingredient 2 and 4 pounds of ingredient 1 should be used to satisfy the imposed conditions.
Solved mentally, using reasoning, ONLY.
Thus, regarding the level of complexity of this problem, it can be solved
by a student of 4-th or 5-th grade, if to get him/her the possibility to think 5 - 10 minutes in a calm environment.
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