A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 35 pounds of phosphoric acid, 15
pounds of nitrogen, and 16 pounds of potash. Each cubic yard of mix B contains 14 pounds of phosphoric acid, 18 pounds of nitrogen, and 64 pounds of potash. The minimum monthly requirements are 840 pounds of phosphoric acid, 540 pounds of nitrogen, and 768 pounds of potash. If x is the number of cubic yards of mix A used and y is the number of cubic yards of mix B used, write a system of linear inequalities that indicates appropriate restraints on x and y. Find the set of feasible solutions graphically for the amounts of mix A and mix B that can be used.
1 answer:
Answer:
The answer is below
Step-by-step explanation:
Given that the minimum monthly requirements are 840 pounds of phosphoric acid, hence:
35 pounds of phosphoric acid mix A + 14 pounds of phosphoric acid mix B ≥ 840 pounds of phosphoric acid
35x + 14y ≥ 840
The minimum monthly requirements are 540 pounds of nitrogen, hence:
15 pounds of nitrogen mix A + 18 pounds of nitrogen mix B ≥ 540 pounds of nitrogen
15x + 18y ≥ 540
The minimum monthly requirements are 768 pounds of potash, hence:
16 pounds of potash mix A + 64 pounds of potash mix B ≥ 768 pounds of potash
16x + 64y ≥ 768
Also, x ≥ 0 and y ≥0.
Therefore the equations are:
35x + 14y ≥ 840
15x + 18y ≥ 540
16x + 64y ≥ 768
x ≥ 0 and y ≥ 0
Plotting with geogebra gives the graph below.
The point are (0,60), (48,0), (18,15), (32,4)
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Answer:
a) 0.194 = 19.4% probability that more than 7 preferred McDonald's
b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's
c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King
Step-by-step explanation:
For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
50% of all young adults prefer McDonald's to Burger King when asked to state a preference.
This means that
12 young adults were randomly selected
This means that
(a) What is the probability that more than 7 preferred McDonald's?
In which
0.194 = 19.4% probability that more than 7 preferred McDonald's
(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?
0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's
(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?
Since , this is the same as b) above.
So
0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King