A manufacturer produces two models of toy airplanes. It takes the manufacturer 20 minutes to assemble model A and 10 minutes to package it. It takes the manufacturer 25 minutes to assemble model B and 5 minutes to package it. In a given week, the total available time for assembling is 3000 minutes, and the total available time for packaging is 1200 minutes. Model A earns a profit of $10 for each unit sold and model B earns a profit of $8 for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week?
Answers
Answer:
[tex]\$1320[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number of units of A
[tex]y[/tex] be the number of units of B
For assembling we have
[tex]20x+25y\leq 3000[/tex]
For packaging we have
[tex]10x+5y\leq 1200[/tex]
Let profits earned be [tex]Z[/tex] so
[tex]Z=10x+8y[/tex]
We have the maximize the function.
Plotting the equations we can see that the intersection points are [tex](0,120),(100,40),(120,0)[/tex]
In the question it is mentioned we have to sell both the products so [tex]x[/tex] or [tex]y[/tex] cannot be [tex]0[/tex].
So, the point of maximiztion for the function would be [tex](100,40)[/tex]
The maximum profit would be
[tex]Z=10\times 100+8\times 40\\\Rightarrow Z=1320[/tex]
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Step-by-step explanation:
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Answer:
No real roots
Step-by-step explanation:
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Lani has 84 Lego blocks and 25% were red. How many red Lego blocks does Lani have? Show and explain your work.
Answers
Answer:
21
Step-by-step explanation:
84x0.25=21
25% is 0.25 as a decimal. Multiply it times 84 to find the answer.
Find the least number which when divided by 12 and 16 leaves the reminder 3 and 7 respectively. Plzz help in this question
Answers
==============================================
Explanation:
Let n be the number we want to find. We want n to be as small as possible, but also be a positive integer. Intuitively, we can see that n cannot be smaller than 16; otherwise, we don't meet the remainder requirements.
Divide n over 12 and we get some quotient x and remainder 3
So,
n/12 = (quotient) + (remainder)/12
n/12 = x + 3/12
Multiply both sides by 12 to end up with
n = 12x + 3
Similarly, if we divide over 16 we get some other quotient y and remainder 7
n/16 = y + 7/16
which turns into
n = 16y + 7
after multiplying both sides by 16
-----------
We have these two equations
n = 12x+3n = 16y+7Apply substitution and do a bit of rearranging like so
12x+3 = 16y+7
12x-16y = 7-3
4(3x-4y) = 4
3x-4y = 4/4
3x-4y = 1
The goal from here is to find the smallest positive integers x and y that make that equation true. We have a few options here and they are
Guess and check: We have a small sample size to work with so it shouldn't take too long. Make a table of xy values where you have x along the top row and y along the left column. Then plug each x,y pair into the equation above to see if you get a true statement or not. Again, keep in mind that x and y are positive integers. Graphing: Graph the line 3x-4y = 1, which is the same as y = (3/4)x - 1/4 and note where the line lands on a lattice point. Focus on the upper right quadrant of the graph. This quadrant is above the x axis and to the right of the y axis.Extended Euclidean Algorithm: This method is the most efficient, but it's only useful if your teacher has gone over it.Whichever method you use, you should find that (x,y) = (3,2) is the point we want.
Note how:
3x-4y = 1
3(3)-4(2) = 1
9-8 = 1
1 = 1
So that verifies (3,2) is on the line 3x-4y = 1.
Because x = 3 and y = 2, we know that
n = 12x + 3
n = 12*3 + 3
n = 39
and we can see that
n = 16y + 7
n = 16*2 + 7
n = 39
So 39 is the smallest such integer such that when we divide it over 12 and 16, we get remainders 3 and 7 respectively.
Here's a quick verification that we've fit the requirements.
39/12 = 3 remainder 3
39/16 = 2 remainder 7
We know we hit the smallest value of n because (x,y) was made to be the smallest positive integer solution to 3x-4y = 1. There are infinitely many positive integer (x,y) solutions to 3x-4y = 1, which in turn means there are infinitely many numbers n that satisfy the remainder conditions (but n is not the smallest possible in those cases).
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answers
Plug in the x and y
(2*9)+(4*-3)= 18-12= 6
(6*9)+(14*-3)= 54-42= 12
6
3. Javon, Sam, and Antoine are baking cookies. Javon
has 1/2 cup of flour, Sam has 14 cups of flour, and
Antoine has 1 cups of flour. How many cups of
flour do they have altogether?
Answers
Answer:
15.5 or 15 and a half cups of flour
Step-by-step explanation:
1/2 = 0.5
14 + 0.5 + 1 = 15.5
Answer: 3 5/12
or
2 17/12
Step-by-step explanation:
hope this helped!!
A new store is handing out small gifts to the customers who come in. Elizabeth is handing out pens of various colors. She has determined that the chance of a customer receiving a blue pen is 0.008. Ricardo is handing out tote bags of various colors He has determined that the chance of a customer receiving a blue tote bag is 0.04. What statement describes the likelihood of a customer getting a blue tote bag or blue pen?
Answers
Answer:
4.8% probability of a customer getting a blue tote bag or blue pen.
Step-by-step explanation:
We have these following probabilities:
0.008 probability of a customer receiving a blue pen.
0.04 probability of a customer receiing a blue tote bag.
What statement describes the likelihood of a customer getting a blue tote bag or blue pen?
Independent events, so
0.008 + 0.04 = 0.048 = 4.8% probability of a customer getting a blue tote bag or blue pen.
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Answers
Answer:
Q = 85°
Step-by-step explanation:
P + Q = 180° (angles on the same side of transversal)
95° + Q = 180°
Q = 180° - 95°
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A.
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B.
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Answers
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Answers
Answer:
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Step-by-step explanation:
Given
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:x=31
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Step-by-step explanation:
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Answers
Answer:
A = 117in²
Step-by-step explanation:
A = bh
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A = 117in²
13
×9
117
Since it's a parallelogram where going to do the formula b×h.
Answer:
117in²
Step-by-step explanation:
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Answers
Answer:
C meter
Step-by-step explanation
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Answers
Answer:
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Step-by-step explanation:
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Answers
the answer is:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
D. 1/15
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answers
No Solution!
Step-by-step explanation:
If we make a graph of the given equations the equation's lines will be parallel. We know that, when the lines are parallel, there is no solution.
Answer:
I think it has only one solution
A suitcase is discounted 40 % off the original price, p . Which expression represents the price of the suitcase with the discount?
Answers
Answer:
Step-by-step explanation:
b
0.6p is the expression represents the price of the suitcase with the discount
How to calculate perecent discountHow can I figure out a discount of X%?You apply the fundamental formula given above in this situation.Take the original cost.The result is multiplied by the discount and divided by 100.Subtract the updated amount from the starting cost.Your total price is that. Enjoy your discounts!To learn more about discount, refer to https://brainly.com/question/1548141
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Please tell the answer
Answers
Answer:
Step-by-step explanation:
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<ABO also = 40 (the triangle is isosceles by two legs being radii).
That means that BOA = 180 - 40 - 40 = 100
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20 feet
Lucy<-] 0
1
14 feet
Grace
To the nearest degree, what is the measure of the angle of depression?
Answers
Answer:
35
Step-by-step explanation:
The answer is 35 degrees
Which equation shows the line with m = 6 and Y - intercept = -3,
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Answers
Answer:
y = 6x - 3
Step-by-step explanation:
The equation shows the line with slope of 6 and y-intercept = -3 will be y = 6x - 3.
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The linear equation is given as,
y = mx + c
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The slope of the line is 6 and the y-intercept of the line is negative 3. Then the equation of the line will be
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A rectangular flag has an area of 3/8 square foot. The width is 3/4 foot. What is the length of the flag?
Answers
Answer:
1/2
Step-by-step explanation:
Area= 3/8
Width=3/4
Length=?
3/8=0.375
3/4x1/2=3/8 (0.375)
Please help!! due today
Answers
Answer:
5f + 6g + 12
Step-by-step explanation:
10f - 5f is 5f, you would keep 6g as it is because there are no other numbers to add to it, and 8 + 4 is 12. Hope this helps!! :)
P = 2l + 2w, when P = 28 ft. and w = 5 ft.
Answers
Answer:
9
Step-by-step explanation:
5*2=10 28-10=18 18/2=9