Kelly runs a restaurant that sells two kinds of desserts. Kelly knows the restaurant must make at least 25 dozen and at most 45
dozen White Chocolate Blizzards. The restaurant must also make at least 2 dozen and at most 15 dozen Mint Breezes. Each dozen of White Chocolate Blizzards takes 5 ounces, of flour, while each dozen of Mint Breezes requires 9 ounces of flour. The restaurant only has 315 ounces of flour available. If a dozen White Chocolate Blizzards generate $2.92 in income, and a dozen Mint Breezes generate $2.11, how many dozens of the desserts should Kelly have the restaurant make to maximize income? Express your answer as an ordered pair in the form (c,m) where c represents dozens of White Chocolate Blizzards and m represents dozens of Mint Breezes.
1 answer:
Answer:
(c, m) = (45, 10)
Step-by-step explanation:
A dozen White Chocolate Blizzards generate more income and take less flour than a dozen Mint Breezes, so production of those should clearly be maximized. Making 45 dozen Blizzards does not use all the flour, so the remaining flour can be used to make Breezes.
Maximum Blizzards that can be made: 45 dz. Flour used: 45×5 oz = 225 oz.
The remaining flour is ...
315 oz -225 oz = 90 oz
This is enough for (90 oz)/(9 oz/dz) = 10 dozen Mint Breezes. This is in the required range of 2 to 15 dozen.
Kelly should make 45 dozen White Chocolate Blizzards and 10 dozen Mint Breezes: (c, m) = (45, 10).
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In the attached graph, we have reversed the applicable inequalities so the feasible region shows up white, instead of shaded with 5 different colors. The objective function is the green line, shown at the point that maximizes income. (c, m) ⇔ (x, y)
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Answer: 90
Step-by-step explanation:
The formula for calculating the nth term of a sequence is given as :
= a + ( n - d )
Where a is the first term
d is the common difference and
n is the number of terms
This means that the 4th term of an arithmetic sequence will have the formula :
= a + 3d
And the 4th term has been given to be , 12 ,substituting into the formula we have
12 = a + 3d .............................. equation 1
Also substituting for the 8th term , we have
36 = a + 7d .............................. equation 2
Combining the two equations , we have
a + 3d = 12 ................... equation 1
a + 7d = 36 ------------ equation 2
Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is
a = 12 - 3d ................... equation 3
substitute a = 12 - 3d into equation 2 , equation 2 then becomes
12 - 3d + 7d = 36
12 + 4d = 36
subtract 12 from both sides
4d = 36 - 12
4d = 24
divide through by 4
d = 6
substitute d = 6 into equation 3 to find the value of a, we have
a = 12 - 3d
a = 12 - 3 ( 6)
a = 12 - 18
a = -6
Therefore , the 17th term of the sequence will be :
= a + 16d
= -6 + 16 (6)
= -6 + 96
= 90
Therefore : the 17th term of the sequence is 90
The property used to rewrite the given expression is product property.
Answer: Option A
<u>Step-by-step explanation:</u>
Given equation:
The sum of the two logarithms of two quantities (on the same basis) corresponds to the logarithm of their product on the same basis. The product log is equal to the log’s sum of the factors.
There are several rules that you can use to solve logarithmic equations. One of these guidelines is the logarithmic products rule that you can use to differentiate complex protocols in different ways. Different values that can be valuable are the quota principle and the logarithm rule. The logarithmic products rule is essential and is regularly used in analysis to control logs and simplify baseline conditions.