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2 answers:
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I like to use an X diagram to solve problems like this. The constituent percentages are on the left, the desired mix is in the middle and the numbers on the diagonals are the difference between the mix and the constituent.
The numbers 6 and 24 here represent the ratio of 40% to 10% chocolate. That 6:24 ratio can be reduced to 1:4. The sum of those ratio units is 1+4 = 5, so each must represent (200 kg)/5 = 40 kg of chocolate.
The mix must consist of
40 kg of 40% fat chocolate
160 kg of 10% fat chocolate
The numbers 6 and 24 here represent the ratio of 40% to 10% chocolate. That 6:24 ratio can be reduced to 1:4. The sum of those ratio units is 1+4 = 5, so each must represent (200 kg)/5 = 40 kg of chocolate.
The mix must consist of
40 kg of 40% fat chocolate
160 kg of 10% fat chocolate
Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
-----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
-----> inequality B
Remember that P(x) is in thousands of dollars
Solve the system by graphing
using a graphing tool
The solution is the interval [6.78,39.22]
see the attached figure
therefore
A reasonable constraint for the model is
6.84 ≤ x ≤ 37.39
