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]
Related Questions
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).
I don't get this question
Answers
Answer:
Q = 85°
Step-by-step explanation:
P + Q = 180° (angles on the same side of transversal)
95° + Q = 180°
Q = 180° - 95°
Q = 85°
Am I correct? (Perfect Square Form)
Answers
Answer:
[tex](x -3 )^2 = 10[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 6x - 1 = 0[/tex]
Required: Express as a perfect square
[tex]x^2 - 6x - 1 = 0[/tex]
Add 10 to both sides
[tex]x^2 - 6x - 1 +10= 0+10[/tex]
[tex]x^2 - 6x +9= 10[/tex]
Expand
[tex]x^2 - 3x - 3x+9= 10[/tex]
Factorize:
[tex]x(x - 3) - 3(x - 3)= 10[/tex]
Factorize:
[tex](x -3 )(x - 3) = 10[/tex]
[tex](x -3 )^2 = 10[/tex]
right and evaluate an expression to help you determine how much you make if you charge $7.50 to walk dogs and you walk 10 dogs
Answers
Answer:
7.50(10)
You make 75 dollars
Step-by-step explanation:
7.50(10)= 75
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!! :)
A truck can travel 12 miles on a gallon of gasoline. How far can the truck travel on 40 gallons of gasoline? Which operation is best to answer this question?
Answers
Answer:
im sorry
Step-by-step explanation:
i dont kno
A biologist is growing a population of bacteria for a study. The number of millions of bacteria in the population is modeled by a function, f(x), where x is the number of days since yesterday. The table shows values of f(x) for different values of x.
x f(x)
−2 3.25
−1 3.5
0 4
2 7
4 19
The function f(x) can be represented by the equation f(x)=ax+b. Enter the value for a and b in the equation f(x)=ax+b.
Answers
Answer:
y = 2x
Step-by-step explanation:
Complete a table of values for –2 < x < 2. Connect the points on the graph with a smooth curve.
Please help me with this question
Answers
It is Called because 627 times 35 equals 21,945.
Question 7. Jose has scored 874 points on his math tests so far this semester. To get an A for the semester, he must score at least 959 points. Part 1 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests. What is the inequality. What is the solution to the inequality
Answers
Answer:
Step-by-step explanation: How many more points does he need to get to 959
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.
can somebody please help me write an algebraic expression for the word problem “the quotient of a number and 12”
Answers
Answer:
n/12
Step-by-step explanation:
Please tell the answer
Answers
Answer:
Step-by-step explanation:
The person I sent it to couldn't see it either. I'm going to take a chance and say the Chord (AB) and the Tangent line form a 50 degree angle. If this is incorrect, I won't know, from the diagram, what else to try.
If I'm right then <OAB = 40 degrees because 90 - 50 = 40 because <AOC is a right angle (property of radii and tangents).
<ABO also = 40 (the triangle is isosceles by two legs being radii).
That means that BOA = 180 - 40 - 40 = 100
AE←→ is a straight line in the diagram.
What is the sum of the measures that represent the measures of each angle if m∠ABC=2x°, m∠CBD=3x°, and m∠EBD=4x°?
What is the measure of each angle?
Explain how an equation can be written to find m∠CBD.
Answers
Answer:
hwqvh bjvs bhs ebf
Step-by-step explanation:
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
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.
2. The actual tree on the left is 10 feet tall. The model tree on the right is 8 inches tall. What is the scale factor?
A: 15 B: 112 C: 1/122 D: 1/15
Answers
Answer:
D. 1/15
Step-by-step explanation:
Actual tree = 10 ft = 12 × 10 = 120 in.
Model tree = 8 in.
Scale factor = model tree/actual tree
Scale factor = 8/120
Scale factor = 1/15
Sue walks 1 mile to a store. About how far is this in metric units? A. 2 millimeters B. Centimeters C. 2 meters D. Kilometers please help if you can! :D
Answers
Answer:
C meter
Step-by-step explanation
Did this in class luv hope this helps<3
Lucy is standing on a balcony looking down at her friend Grace, as shown in the diagram.
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
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!!
Which equation shows the line with m = 6 and Y - intercept = -3,
written in slope-intercept form?
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.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
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
y = 6x - 3
The equation shows the line with slope of 6 and y-intercept = -3 will be y = 6x - 3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
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
#SPJ1
Dylan opened a credit card account with $700,00 of available credit. Now that he has made
some purchases, Dylan's account only has $539.00 of available credit. What is the percentage
decrease of the amount of available credit in Dylan's account?
A.
23%
B.
17%
C.
30%
D.
77%
Answers
539 divided by 700 is .77
Which is 77% of the original
So 100-77 is 23%
Find the area of the parallelogram.
The area of the parallelogram is [a] in2.
Answers
Answer:
A = 117in²
Step-by-step explanation:
A = bh
A = 9×13
A = 117in²
13
×9
117
Since it's a parallelogram where going to do the formula b×h.
Answer:
117in²
Step-by-step explanation:
Two lines Intersect at one polnt.
True
False
Answers
the answer is:
Trueeeee
Answer:
False
Step-by-step explanation:
IF the lines are parallel, they will NEVER intersect at any point at any time. I hope this helps :)
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
What is the value of x?
Answers
Answer:x=31
not sure
Step-by-step explanation:
help me with this root problem....
Answers
Answer:
No real roots
Step-by-step explanation:
When graphed, doesn't cross the x-axis
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
A circular pond has a radius of 6m. Calculate the circumference of the pond. Give your answer rounded to the nearest tenth.
Answers
Answer:
37.7
Step-by-step explanation:
C= 2(3.14)6
C = 6.28(6)
C= 37.68
C= 37.7
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)