Roger sells fire trucks and dolls to a toy store. He sells each fire truck for $15 and each doll for $10. Roger wants to sell at least 25 toys and needs to earn at least $300 to cover his costs. If each fire truck takes 50 minutes to make and each doll takes 45 minutes to make, how many fire trucks and dolls should Roger make to minimize the time spent making the toys.
Answers
Answer:
this is the correct answer for plato (Roger should make 10 fire trucks and 15 dolls in order to minimize the time spent making toys.)
Step-by-step explanation:
Answer:
Number of Fire trucks made= 10.
Number of Dolls made = 15
Step-by-step explanation:
Let x denote the number of fire trucks made.
and y denote the number of dolls made.
Now we are given:
Roger wants to sell at least 25 toys .Hence, the inequality that can be made from this information is:
[tex]x+y\geq 25[/tex]
Also,He sells each fire truck for $15 and each doll for $10.
He needs to earn at least $300 to cover his costs.
The inequality that can be made from this piece of information is:
[tex]15x+10y\geq 300[/tex]
Also,
x≥0
and y≥0
Each fire truck takes 50 minutes to make and each doll takes 45 minutes to make.
Now we are asked to minimize the time function let it denote by 'z'.
Hence, the system that is formed is:
Optimization function Min. z=50x+45y
subject to x+y ≥ 25[/tex]
and 15x+10y ≥ 300[/tex]
Non-negative constraint x ≥ 0
y ≥ 0
Now on solving the constraints we get the boundary points as:
(25,0) , (0,30) and (10,15)
Hence, the optimal solution is checked at these points.
(25,0) z=1250
(0,30) z=1350
(10,15) z=1175
Hence, the minimal time spent is: 1175 minutes.
Number of Fire trucks made= 10.
Number of Dolls made =15
Related Questions
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Answers
455 = 48k
k = 455 / 48 = 9.479
Required equation is n = 9.479 t Answer
The graph will be a straight line passing through the origin with slope 9.479.
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Answer:
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Step-by-step explanation:
Time measured in minutes is an example of a(n) _______________ scale.
Answers
The answer can be written in statement form as,"Time measured in minutes is an example of a(n) interval scale."
What is an interval scale?A numerical scale known as an interval scale is one in which both the order of the variables and their differences are known. Using the Interval scale, variables with recognizable, consistent, and calculable differences are categorized.
It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.
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Find f(5) for f(x). ... .. ... ....
Answers
Maree is 8 years older than Aaron.
Aaron is twice as old as Rick.
All their ages add up to 28.
What are their ages?
Maree is
Aaron is
Rick is
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Answers
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Any proposed solution of a rational equation that causes a denominator to equal _______ is rejected.
Answers
Answer:
Any proposed solution of a rational equation that causes a denominator to equal __ZERO__ is rejected.
Step-by-step explanation:
We will show this statement is true by an example:
Consider the expression : [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Now, solved the rational expression and check its proposed solution
[tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
x cannot equal to 4, as it makes both denominators equal to zero.
Multiply both the sides by (x-4),
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot\left ( \frac{x}{x-4}+4 \right )\\[/tex]
Now, use the distributive property on Right hand side,
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot \left ( \frac{x}{x-4} \right )+\left (x-4 \right )\cdot 4\\[/tex]
Simplify the above expression,
[tex]x=x+4x-16[/tex]
Combine like terms,
[tex]x-x-4x=-16[/tex]
[tex]-4x=-16[/tex]
Divide both sides by -4, we get
[tex]\frac{-4x}{-4}=\frac{-16}{-4}[/tex]
[tex]x=4[/tex].
As we know that x cannot equal to 4, replacing x=4 in the original expression causes the denominator equal to 0.
Check the solution: [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Substitute the value of x=4 in the original expression,
[tex]\frac{4}{4-4}=\frac{4}{4-4}+4[/tex]
[tex]\frac{4}{0}=\frac{4}{0}+4[/tex]
Thus, 4 must be rejected as the solution, and the solution set is only 0.
A proposed solution of a rational equation that causes a denominator to equal zero is rejected because division by zero is not possible.
Explanation:Any proposed solution of a rational equation that causes a denominator to equal zero is rejected. When the denominator of a rational equation is zero, the fraction becomes undefined because division by zero is not possible. In mathematics, division by zero is an undefined operation.
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Answers
Answer: 120 different combinations .
Step-by-step explanation:
The combination of n things taking m things at a time is given by :-
[tex]C(n,m)=\dfrac{n!}{m!(n-m)!}[/tex]
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Answers
Answer:
True
Step-by-step explanation:
Ceremonies do help individuals cope with loss as they facilitate the grieving process.
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $3 for each line. Then the cost to place an ad x lines long is given by y dollars, where y=3x+25. Express an ordered pair the fact that a 2 line ad cost $31
Answers
y = 3(2) + 25
y = 6 + 25
y = 31
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An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 145 for 5 < x ≤ 6
B. C(t) = 145 for 6 < x ≤ 7
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Answers
C(t) = 45 + 25(h-1) where h is the number of hours worked.
We can check for each option in turn:
Option A:
Inequality 5 < x ≤ 6 means the hour is between 5 hours (not inclusive) to 6 hours (inclusive)
Let's take the number of hours = 5
C(5) = 45 + (5-1)×25 = 145
Let's take the number of hours = 6
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We can't take 145 because the value '5' was not inclusive.
Option B:
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We take number of hours = 6
C(6) = 25(6-1) + 45 = 170
We take number of hours = 7
Then C(7) = 25(7-1) + 45 = 195
Option C:
The inequality is 5 < x ≤ 6
Take the number of hours = 5
C(5) = 25(5-1) + 45 = 145
Take the number of hours = 6
C(6) = 25(6-1) + 45 = 170
We can't take the value 145 as '5' was not inclusive in the range, but we can take 170
Option D:
6 < x ≤ 7
25(6-1) + 45 < C(t) ≤ 25(7-1) + 45
170 < C(t) ≤ 195
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Answers
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Answers
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Answers
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thus
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as far as 5, is correct, however
[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{15^2+8^2}\implies c=\sqrt{289}\implies c=17[/tex]
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The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.
Explanation:To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:
x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
Simplifying further, we have:
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.
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